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Номер 13.9, страница 80 - гдз по физике 8-11 класс учебник, задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Учебник, задачник
Издательство: Илекса
Год издания: 2005 - 2026
Цвет обложки: синий мужчина в красном, летит на черном шаре
ISBN: 978-5-89237-332-6
Популярные ГДЗ в 8 классе
Задачи. Электричество и магнетизм. 13. Законы постоянного тока - номер 13.9, страница 80.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-9" "field_display_title" => "13.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:3 [ 0 => App\Models\Branch {#1123 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Book {#1125 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:4 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1130 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ …6] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1132 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ …6] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:3 [ 0 => App\Models\Term {#1136 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1138 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, zadachnik" ] #original: array:10 [ "id" => 6673 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник, задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik, zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Term {#1145 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Term {#1151 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #original: array:6 [ "id" => 35 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "исправленное" "field_cases" => array:6 [ …6] "field_translit" => "ispravlennoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1152 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Term {#1157 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 5401 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1127} "field_class" => Illuminate\Database\Eloquent\Collection {#1128} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133} "field_author" => Illuminate\Database\Eloquent\Collection {#1135} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1139} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1140} "field_country" => Illuminate\Database\Eloquent\Collection {#1142} "field_city" => Illuminate\Database\Eloquent\Collection {#1144} "field_series" => Illuminate\Database\Eloquent\Collection {#1146} "field_umk" => Illuminate\Database\Eloquent\Collection {#1147} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1148} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1149} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1150} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1152} "field_under_the_edition_degree" => null "field_cover_description" => "мужчина в красном, летит на черном шаре" "field_publication_year" => "2005" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1001" "field_priority" => null "field_default_folder" => "/fizika_08/gelfgat-u/" "field_isbn" => "978-5-89237-332-6" "field_cover" => array:1 [ 0 => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gelfgat-u/covers/cover1.webp?ts=1755898771" "alt" => "" "width" => "1813" "height" => "2441" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1153} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1154} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1155} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1156} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287866 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1124} "field_page_start" => "5" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1160} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1158} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1159 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "68" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ 0 => App\Models\Book {#1125} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1163 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1161} "field_page_start" => "68" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1162} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1163} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1164 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287882 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "13. Законы постоянного тока" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1165 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "79" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1166 #items: array:1 [ 0 => App\Models\Book {#1125} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1175 #items: array:1 [ 0 => App\Models\Branch {#1174 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_page_start" => "68" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1178 …2} ] #original: array:24 [ "id" => 1287880 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электричество и магнетизм" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_page_start" => "68" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1178 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1287882 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "13. Законы постоянного тока" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1165} "field_page_start" => "79" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1166} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1175} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:3 [ 0 => App\Models\Element {#1103 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1478542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1104 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "text" => "<p><strong>13.9.</strong> Какие сопротивления $\text{R}$ можно получить, используя не более четырех резисторов с сопротивлением $R_0$? Начертите соответствующие схемы соединений.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1471" "height" => 231 "path" => "/media/fizika_08/gelfgat-u/0-13/9-1.webp?ts=1756049943" ] ] ] #original: array:7 [ "id" => 1478542 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "text" => "<p><strong>13.9.</strong> Какие сопротивления $\text{R}$ можно получить, используя не более четырех резисторов с сопротивлением $R_0$? Начертите соответствующие схемы соединений.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1471" "height" => 231 "path" => "/media/fizika_08/gelfgat-u/0-13/9-1.webp?ts=1756049943" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1098 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1479030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1095 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5411 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1402" "height" => 714 "path" => "/media/fizika_08/gelfgat-u/1-13/9-1.webp?ts=1756050016" ] ] ] #original: array:6 [ "id" => 1479030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1402" "height" => 714 "path" => "/media/fizika_08/gelfgat-u/1-13/9-1.webp?ts=1756050016" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1090 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1738153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Edition {#1089 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6336 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Количество одинаковых резисторов: $1 \le n \le 4$.</p><p>Сопротивление каждого резистора: $R_0$.</p><p><strong>Найти:</strong></p><p>Все возможные значения эквивалентного сопротивления $\text{R}$ цепи.</p><p><strong>Решение:</strong></p><p>Рассмотрим все возможные схемы соединений для количества резисторов $\text{n}$ от 1 до 4.</p><p><strong>ИСПОЛЬЗУЯ ОДИН РЕЗИСТОР (n=1)</strong></p><p><strong>1.</strong> Один резистор</p><p>При использовании одного резистора его сопротивление и будет сопротивлением цепи.</p><p>$R = R_0$</p><p><svg width="120" height="40" style="vertical-align: middle;"><circle cx="10" cy="20" r="3" fill="black"></circle><line x1="13" y1="20" x2="30" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="97" y2="20" stroke="black" stroke-width="2"></line><circle cx="100" cy="20" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $R_0$.</p><p><strong>ИСПОЛЬЗУЯ ДВА РЕЗИСТОРА (n=2)</strong></p><p><strong>1.</strong> Последовательное соединение</p><p>При последовательном соединении общее сопротивление равно сумме сопротивлений: $R = R_0 + R_0 = 2R_0$.</p><p><svg width="180" height="40" style="vertical-align: middle;"><circle cx="10" cy="20" r="3" fill="black"></circle><line x1="13" y1="20" x2="30" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="90" y2="20" stroke="black" stroke-width="2"></line><rect x="90" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="140" y1="20" x2="157" y2="20" stroke="black" stroke-width="2"></line><circle cx="160" cy="20" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $2R_0$.</p><p><strong>2.</strong> Параллельное соединение</p><p>При параллельном соединении: $\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} = \frac{2}{R_0}$, откуда $R = \frac{R_0}{2}$.</p><p><svg width="140" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="60" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="60" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="90" y1="20" x2="90" y2="40" stroke="black" stroke-width="2"></line><line x1="90" y1="60" x2="90" y2="40" stroke="black" stroke-width="2"></line><line x1="90" y1="40" x2="107" y2="40" stroke="black" stroke-width="2"></line><circle cx="110" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{R_0}{2}$.</p><p><strong>ИСПОЛЬЗУЯ ТРИ РЕЗИСТОРА (n=3)</strong></p><p><strong>1.</strong> Последовательное соединение</p><p>$R = R_0 + R_0 + R_0 = 3R_0$.</p><p><strong>Ответ:</strong> $3R_0$.</p><p><strong>2.</strong> Параллельное соединение</p><p>$\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} + \frac{1}{R_0} = \frac{3}{R_0}$, откуда $R = \frac{R_0}{3}$.</p><p><strong>Ответ:</strong> $\frac{R_0}{3}$.</p><p><strong>3.</strong> Смешанное соединение: два параллельно, один последовательно</p><p>Сопротивление двух параллельных резисторов $R_{12} = \frac{R_0}{2}$. Общее сопротивление: $R = R_{12} + R_0 = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$.</p><p><svg width="200" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="60" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="40" x2="100" y2="40" stroke="black" stroke-width="2"></line><rect x="100" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="40" x2="167" y2="40" stroke="black" stroke-width="2"></line><circle cx="170" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{3}{2}R_0$.</p><p><strong>4.</strong> Смешанное соединение: два последовательно, один параллельно</p><p>Сопротивление двух последовательных резисторов $R_{12} = 2R_0$. Общее сопротивление: $\frac{1}{R} = \frac{1}{R_{12}} + \frac{1}{R_0} = \frac{1}{2R_0} + \frac{1}{R_0} = \frac{3}{2R_0}$, откуда $R = \frac{2}{3}R_0$.</p><p><svg width="180" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="40" y="14" width="40" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="90" y2="20" stroke="black" stroke-width="2"></line><rect x="90" y="14" width="40" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="30" y1="20" x2="40" y2="20" stroke="black" stroke-width="2"></line><line x1="130" y1="20" x2="140" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="54" width="110" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="140" y1="20" x2="140" y2="40" stroke="black" stroke-width="2"></line><line x1="140" y1="60" x2="140" y2="40" stroke="black" stroke-width="2"></line><line x1="140" y1="40" x2="157" y2="40" stroke="black" stroke-width="2"></line><circle cx="160" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{2}{3}R_0$.</p><p><strong>ИСПОЛЬЗУЯ ЧЕТЫРЕ РЕЗИСТОРА (n=4)</strong></p><p>Помимо очевидных случаев (все последовательно и все параллельно), существует несколько вариантов смешанного соединения.</p><p><strong>1. Последовательное соединение:</strong> $R = 4R_0$.</p><p><strong>Ответ:</strong> $4R_0$.</p><p><strong>2. Параллельное соединение:</strong> $R = \frac{R_0}{4}$.</p><p><strong>Ответ:</strong> $\frac{R_0}{4}$.</p><p><strong>3. Три параллельно, один последовательно:</strong> $R = \frac{R_0}{3} + R_0 = \frac{4}{3}R_0$.</p><p><strong>Ответ:</strong> $\frac{4}{3}R_0$.</p><p><strong>4. Три последовательно, один параллельно:</strong> $\frac{1}{R} = \frac{1}{3R_0} + \frac{1}{R_0} = \frac{4}{3R_0} \implies R = \frac{3}{4}R_0$.</p><p><strong>Ответ:</strong> $\frac{3}{4}R_0$.</p><p><strong>5. Два параллельно, последовательно с двумя последовательными:</strong> $R = \frac{R_0}{2} + R_0 + R_0 = \frac{5}{2}R_0$.</p><p><svg width="240" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="60" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="40" x2="100" y2="40" stroke="black" stroke-width="2"></line><rect x="100" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="40" x2="160" y2="40" stroke="black" stroke-width="2"></line><rect x="160" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="210" y1="40" x2="227" y2="40" stroke="black" stroke-width="2"></line><circle cx="230" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{5}{2}R_0$.</p><p><strong>6. Два последовательно, параллельно с двумя параллельными:</strong> $\frac{1}{R} = \frac{1}{2R_0} + \frac{1}{R_0/2} = \frac{1}{2R_0} + \frac{2}{R_0} = \frac{5}{2R_0} \implies R = \frac{2}{5}R_0$.</p><p><svg width="220" height="100" style="vertical-align: middle;"><circle cx="10" cy="50" r="3" fill="black"></circle><line x1="13" y1="50" x2="30" y2="50" stroke="black" stroke-width="2"></line><line x1="30" y1="50" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="50" x2="30" y2="80" stroke="black" stroke-width="2"></line><line x1="30" y1="20" x2="40" y2="20" stroke="black" stroke-width="2"></line><rect x="40" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="90" y1="20" x2="100" y2="20" stroke="black" stroke-width="2"></line><rect x="100" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="20" x2="180" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="80" x2="60" y2="80" stroke="black" stroke-width="2"></line><line x1="60" y1="80" x2="60" y2="65" stroke="black" stroke-width="2"></line><line x1="60" y1="80" x2="60" y2="95" stroke="black" stroke-width="2"></line><rect x="60" y="59" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="60" y="89" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="110" y1="65" x2="110" y2="80" stroke="black" stroke-width="2"></line><line x1="110" y1="95" x2="110" y2="80" stroke="black" stroke-width="2"></line><line x1="110" y1="80" x2="180" y2="80" stroke="black" stroke-width="2"></line><line x1="180" y1="20" x2="180" y2="50" stroke="black" stroke-width="2"></line><line x1="180" y1="80" x2="180" y2="50" stroke="black" stroke-width="2"></line><line x1="180" y1="50" x2="197" y2="50" stroke="black" stroke-width="2"></line><circle cx="200" cy="50" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{2}{5}R_0$.</p><p><strong>7. Цепочка из двух параллельных и одного последовательного, параллельно с четвертым:</strong> $R' = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$. Тогда $\frac{1}{R} = \frac{1}{R'} + \frac{1}{R_0} = \frac{1}{3R_0/2} + \frac{1}{R_0} = \frac{2}{3R_0} + \frac{3}{3R_0} = \frac{5}{3R_0} \implies R = \frac{3}{5}R_0$.</p><p><strong>Ответ:</strong> $\frac{3}{5}R_0$.</p><p><strong>8. Блок из двух последовательных и одного параллельного, последовательно с четвертым:</strong> $R' = \frac{2}{3}R_0$. Тогда $R = R' + R_0 = \frac{2}{3}R_0 + R_0 = \frac{5}{3}R_0$.</p><p><strong>Ответ:</strong> $\frac{5}{3}R_0$.</p><p>Также возможно собрать схему "мост", где все четыре резистора одинаковы. Такое соединение будет иметь эквивалентное сопротивление $R=R_0$, что не является новым значением.</p><p>Соберем все полученные уникальные значения сопротивлений (в долях от $R_0$):</p><p>$\frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, 1, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}, 2, \frac{5}{2}, 3, 4$.</p>" ] #original: array:6 [ "id" => 1738153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1080} "task" => array:2 [ "refs" => "1288460" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Количество одинаковых резисторов: $1 \le n \le 4$.</p><p>Сопротивление каждого резистора: $R_0$.</p><p><strong>Найти:</strong></p><p>Все возможные значения эквивалентного сопротивления $\text{R}$ цепи.</p><p><strong>Решение:</strong></p><p>Рассмотрим все возможные схемы соединений для количества резисторов $\text{n}$ от 1 до 4.</p><p><strong>ИСПОЛЬЗУЯ ОДИН РЕЗИСТОР (n=1)</strong></p><p><strong>1.</strong> Один резистор</p><p>При использовании одного резистора его сопротивление и будет сопротивлением цепи.</p><p>$R = R_0$</p><p><svg width="120" height="40" style="vertical-align: middle;"><circle cx="10" cy="20" r="3" fill="black"></circle><line x1="13" y1="20" x2="30" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="97" y2="20" stroke="black" stroke-width="2"></line><circle cx="100" cy="20" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $R_0$.</p><p><strong>ИСПОЛЬЗУЯ ДВА РЕЗИСТОРА (n=2)</strong></p><p><strong>1.</strong> Последовательное соединение</p><p>При последовательном соединении общее сопротивление равно сумме сопротивлений: $R = R_0 + R_0 = 2R_0$.</p><p><svg width="180" height="40" style="vertical-align: middle;"><circle cx="10" cy="20" r="3" fill="black"></circle><line x1="13" y1="20" x2="30" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="90" y2="20" stroke="black" stroke-width="2"></line><rect x="90" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="140" y1="20" x2="157" y2="20" stroke="black" stroke-width="2"></line><circle cx="160" cy="20" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $2R_0$.</p><p><strong>2.</strong> Параллельное соединение</p><p>При параллельном соединении: $\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} = \frac{2}{R_0}$, откуда $R = \frac{R_0}{2}$.</p><p><svg width="140" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="60" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="60" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="90" y1="20" x2="90" y2="40" stroke="black" stroke-width="2"></line><line x1="90" y1="60" x2="90" y2="40" stroke="black" stroke-width="2"></line><line x1="90" y1="40" x2="107" y2="40" stroke="black" stroke-width="2"></line><circle cx="110" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{R_0}{2}$.</p><p><strong>ИСПОЛЬЗУЯ ТРИ РЕЗИСТОРА (n=3)</strong></p><p><strong>1.</strong> Последовательное соединение</p><p>$R = R_0 + R_0 + R_0 = 3R_0$.</p><p><strong>Ответ:</strong> $3R_0$.</p><p><strong>2.</strong> Параллельное соединение</p><p>$\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} + \frac{1}{R_0} = \frac{3}{R_0}$, откуда $R = \frac{R_0}{3}$.</p><p><strong>Ответ:</strong> $\frac{R_0}{3}$.</p><p><strong>3.</strong> Смешанное соединение: два параллельно, один последовательно</p><p>Сопротивление двух параллельных резисторов $R_{12} = \frac{R_0}{2}$. Общее сопротивление: $R = R_{12} + R_0 = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$.</p><p><svg width="200" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="60" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="40" x2="100" y2="40" stroke="black" stroke-width="2"></line><rect x="100" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="40" x2="167" y2="40" stroke="black" stroke-width="2"></line><circle cx="170" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{3}{2}R_0$.</p><p><strong>4.</strong> Смешанное соединение: два последовательно, один параллельно</p><p>Сопротивление двух последовательных резисторов $R_{12} = 2R_0$. Общее сопротивление: $\frac{1}{R} = \frac{1}{R_{12}} + \frac{1}{R_0} = \frac{1}{2R_0} + \frac{1}{R_0} = \frac{3}{2R_0}$, откуда $R = \frac{2}{3}R_0$.</p><p><svg width="180" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="40" y="14" width="40" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="90" y2="20" stroke="black" stroke-width="2"></line><rect x="90" y="14" width="40" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="30" y1="20" x2="40" y2="20" stroke="black" stroke-width="2"></line><line x1="130" y1="20" x2="140" y2="20" stroke="black" stroke-width="2"></line><rect x="30" y="54" width="110" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="140" y1="20" x2="140" y2="40" stroke="black" stroke-width="2"></line><line x1="140" y1="60" x2="140" y2="40" stroke="black" stroke-width="2"></line><line x1="140" y1="40" x2="157" y2="40" stroke="black" stroke-width="2"></line><circle cx="160" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{2}{3}R_0$.</p><p><strong>ИСПОЛЬЗУЯ ЧЕТЫРЕ РЕЗИСТОРА (n=4)</strong></p><p>Помимо очевидных случаев (все последовательно и все параллельно), существует несколько вариантов смешанного соединения.</p><p><strong>1. Последовательное соединение:</strong> $R = 4R_0$.</p><p><strong>Ответ:</strong> $4R_0$.</p><p><strong>2. Параллельное соединение:</strong> $R = \frac{R_0}{4}$.</p><p><strong>Ответ:</strong> $\frac{R_0}{4}$.</p><p><strong>3. Три параллельно, один последовательно:</strong> $R = \frac{R_0}{3} + R_0 = \frac{4}{3}R_0$.</p><p><strong>Ответ:</strong> $\frac{4}{3}R_0$.</p><p><strong>4. Три последовательно, один параллельно:</strong> $\frac{1}{R} = \frac{1}{3R_0} + \frac{1}{R_0} = \frac{4}{3R_0} \implies R = \frac{3}{4}R_0$.</p><p><strong>Ответ:</strong> $\frac{3}{4}R_0$.</p><p><strong>5. Два параллельно, последовательно с двумя последовательными:</strong> $R = \frac{R_0}{2} + R_0 + R_0 = \frac{5}{2}R_0$.</p><p><svg width="240" height="80" style="vertical-align: middle;"><circle cx="10" cy="40" r="3" fill="black"></circle><line x1="13" y1="40" x2="30" y2="40" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="40" x2="30" y2="60" stroke="black" stroke-width="2"></line><rect x="30" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="30" y="54" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="80" y1="20" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="60" x2="80" y2="40" stroke="black" stroke-width="2"></line><line x1="80" y1="40" x2="100" y2="40" stroke="black" stroke-width="2"></line><rect x="100" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="40" x2="160" y2="40" stroke="black" stroke-width="2"></line><rect x="160" y="34" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="210" y1="40" x2="227" y2="40" stroke="black" stroke-width="2"></line><circle cx="230" cy="40" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{5}{2}R_0$.</p><p><strong>6. Два последовательно, параллельно с двумя параллельными:</strong> $\frac{1}{R} = \frac{1}{2R_0} + \frac{1}{R_0/2} = \frac{1}{2R_0} + \frac{2}{R_0} = \frac{5}{2R_0} \implies R = \frac{2}{5}R_0$.</p><p><svg width="220" height="100" style="vertical-align: middle;"><circle cx="10" cy="50" r="3" fill="black"></circle><line x1="13" y1="50" x2="30" y2="50" stroke="black" stroke-width="2"></line><line x1="30" y1="50" x2="30" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="50" x2="30" y2="80" stroke="black" stroke-width="2"></line><line x1="30" y1="20" x2="40" y2="20" stroke="black" stroke-width="2"></line><rect x="40" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="90" y1="20" x2="100" y2="20" stroke="black" stroke-width="2"></line><rect x="100" y="14" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="150" y1="20" x2="180" y2="20" stroke="black" stroke-width="2"></line><line x1="30" y1="80" x2="60" y2="80" stroke="black" stroke-width="2"></line><line x1="60" y1="80" x2="60" y2="65" stroke="black" stroke-width="2"></line><line x1="60" y1="80" x2="60" y2="95" stroke="black" stroke-width="2"></line><rect x="60" y="59" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><rect x="60" y="89" width="50" height="12" stroke="black" fill="white" stroke-width="2"></rect><line x1="110" y1="65" x2="110" y2="80" stroke="black" stroke-width="2"></line><line x1="110" y1="95" x2="110" y2="80" stroke="black" stroke-width="2"></line><line x1="110" y1="80" x2="180" y2="80" stroke="black" stroke-width="2"></line><line x1="180" y1="20" x2="180" y2="50" stroke="black" stroke-width="2"></line><line x1="180" y1="80" x2="180" y2="50" stroke="black" stroke-width="2"></line><line x1="180" y1="50" x2="197" y2="50" stroke="black" stroke-width="2"></line><circle cx="200" cy="50" r="3" fill="black"></circle></svg></p><p><strong>Ответ:</strong> $\frac{2}{5}R_0$.</p><p><strong>7. Цепочка из двух параллельных и одного последовательного, параллельно с четвертым:</strong> $R' = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$. Тогда $\frac{1}{R} = \frac{1}{R'} + \frac{1}{R_0} = \frac{1}{3R_0/2} + \frac{1}{R_0} = \frac{2}{3R_0} + \frac{3}{3R_0} = \frac{5}{3R_0} \implies R = \frac{3}{5}R_0$.</p><p><strong>Ответ:</strong> $\frac{3}{5}R_0$.</p><p><strong>8. Блок из двух последовательных и одного параллельного, последовательно с четвертым:</strong> $R' = \frac{2}{3}R_0$. Тогда $R = R' + R_0 = \frac{2}{3}R_0 + R_0 = \frac{5}{3}R_0$.</p><p><strong>Ответ:</strong> $\frac{5}{3}R_0$.</p><p>Также возможно собрать схему "мост", где все четыре резистора одинаковы. Такое соединение будет иметь эквивалентное сопротивление $R=R_0$, что не является новым значением.</p><p>Соберем все полученные уникальные значения сопротивлений (в долях от $R_0$):</p><p>$\frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, 1, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}, 2, \frac{5}{2}, 3, 4$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1288461" "type" => "task" ] "previous" => array:2 [ "refs" => "1288459" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Book {#1125} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\BookPage {#1075 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1340431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-80" "field_display_title" => "80" "field_folder" => "1" "field_image_name" => "80" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1125} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:1 [ 0 => App\Models\Element {#1116 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1518552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1167 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1518552 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1167 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1340432" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340430" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1288 #items: array:8 [ 0 => App\Models\Task {#1302 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288454 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_page_end" => "80" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-3" "field_display_title" => "13.3" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1303 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1304 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1305 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1309 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1315 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288454 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_page_end" => "80" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-3" "field_display_title" => "13.3" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1303 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1304 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1305 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1306 …2} "content" => Illuminate\Database\Eloquent\Collection {#1309 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1315 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1308 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288455 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-4" "field_display_title" => "13.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1307 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1314 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1316 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1312 …2} "content" => Illuminate\Database\Eloquent\Collection {#1311 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1329 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288455 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-4" "field_display_title" => "13.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1307 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1314 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1316 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1312 …2} "content" => Illuminate\Database\Eloquent\Collection {#1311 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1329 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1313 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-5" "field_display_title" => "13.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1310 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1328 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1330 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1326 …2} "content" => Illuminate\Database\Eloquent\Collection {#1325 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1343 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-5" "field_display_title" => "13.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1310 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1328 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1330 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1326 …2} "content" => Illuminate\Database\Eloquent\Collection {#1325 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1343 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1327 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1288457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-6" "field_display_title" => "13.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1324 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1342 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1344 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1340 …2} "content" => Illuminate\Database\Eloquent\Collection {#1339 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1357 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1288457 …23 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 4 => App\Models\Task {#1341 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1355 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1369 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1381 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1340431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-80" "field_display_title" => "80" "field_folder" => "1" "field_image_name" => "80" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1078} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1082} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1079} "content" => Illuminate\Database\Eloquent\Collection {#1168} "next" => array:2 [ "refs" => "1340432" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340430" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1288} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1288460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "80" "field_page_end" => null "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/13-9" "field_display_title" => "13.9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1113} "content" => Illuminate\Database\Eloquent\Collection {#1111} "next" => array:2 [ "refs" => "1288461" "type" => "task" ] "previous" => array:2 [ "refs" => "1288459" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1107} "page" => array:2 [ "refs" => "1340431" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№13.9 (с. 80)
Условие. №13.9 (с. 80)
скриншот условия
13.9. Какие сопротивления $\text{R}$ можно получить, используя не более четырех резисторов с сопротивлением $R_0$? Начертите соответствующие схемы соединений.
Решение. №13.9 (с. 80)
Решение 2. №13.9 (с. 80)
Дано:
Количество одинаковых резисторов: $1 \le n \le 4$.
Сопротивление каждого резистора: $R_0$.
Найти:
Все возможные значения эквивалентного сопротивления $\text{R}$ цепи.
Решение:
Рассмотрим все возможные схемы соединений для количества резисторов $\text{n}$ от 1 до 4.
ИСПОЛЬЗУЯ ОДИН РЕЗИСТОР (n=1)
1. Один резистор
При использовании одного резистора его сопротивление и будет сопротивлением цепи.
$R = R_0$
Ответ: $R_0$.
ИСПОЛЬЗУЯ ДВА РЕЗИСТОРА (n=2)
1. Последовательное соединение
При последовательном соединении общее сопротивление равно сумме сопротивлений: $R = R_0 + R_0 = 2R_0$.
Ответ: $2R_0$.
2. Параллельное соединение
При параллельном соединении: $\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} = \frac{2}{R_0}$, откуда $R = \frac{R_0}{2}$.
Ответ: $\frac{R_0}{2}$.
ИСПОЛЬЗУЯ ТРИ РЕЗИСТОРА (n=3)
1. Последовательное соединение
$R = R_0 + R_0 + R_0 = 3R_0$.
Ответ: $3R_0$.
2. Параллельное соединение
$\frac{1}{R} = \frac{1}{R_0} + \frac{1}{R_0} + \frac{1}{R_0} = \frac{3}{R_0}$, откуда $R = \frac{R_0}{3}$.
Ответ: $\frac{R_0}{3}$.
3. Смешанное соединение: два параллельно, один последовательно
Сопротивление двух параллельных резисторов $R_{12} = \frac{R_0}{2}$. Общее сопротивление: $R = R_{12} + R_0 = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$.
Ответ: $\frac{3}{2}R_0$.
4. Смешанное соединение: два последовательно, один параллельно
Сопротивление двух последовательных резисторов $R_{12} = 2R_0$. Общее сопротивление: $\frac{1}{R} = \frac{1}{R_{12}} + \frac{1}{R_0} = \frac{1}{2R_0} + \frac{1}{R_0} = \frac{3}{2R_0}$, откуда $R = \frac{2}{3}R_0$.
Ответ: $\frac{2}{3}R_0$.
ИСПОЛЬЗУЯ ЧЕТЫРЕ РЕЗИСТОРА (n=4)
Помимо очевидных случаев (все последовательно и все параллельно), существует несколько вариантов смешанного соединения.
1. Последовательное соединение: $R = 4R_0$.
Ответ: $4R_0$.
2. Параллельное соединение: $R = \frac{R_0}{4}$.
Ответ: $\frac{R_0}{4}$.
3. Три параллельно, один последовательно: $R = \frac{R_0}{3} + R_0 = \frac{4}{3}R_0$.
Ответ: $\frac{4}{3}R_0$.
4. Три последовательно, один параллельно: $\frac{1}{R} = \frac{1}{3R_0} + \frac{1}{R_0} = \frac{4}{3R_0} \implies R = \frac{3}{4}R_0$.
Ответ: $\frac{3}{4}R_0$.
5. Два параллельно, последовательно с двумя последовательными: $R = \frac{R_0}{2} + R_0 + R_0 = \frac{5}{2}R_0$.
Ответ: $\frac{5}{2}R_0$.
6. Два последовательно, параллельно с двумя параллельными: $\frac{1}{R} = \frac{1}{2R_0} + \frac{1}{R_0/2} = \frac{1}{2R_0} + \frac{2}{R_0} = \frac{5}{2R_0} \implies R = \frac{2}{5}R_0$.
Ответ: $\frac{2}{5}R_0$.
7. Цепочка из двух параллельных и одного последовательного, параллельно с четвертым: $R' = \frac{R_0}{2} + R_0 = \frac{3}{2}R_0$. Тогда $\frac{1}{R} = \frac{1}{R'} + \frac{1}{R_0} = \frac{1}{3R_0/2} + \frac{1}{R_0} = \frac{2}{3R_0} + \frac{3}{3R_0} = \frac{5}{3R_0} \implies R = \frac{3}{5}R_0$.
Ответ: $\frac{3}{5}R_0$.
8. Блок из двух последовательных и одного параллельного, последовательно с четвертым: $R' = \frac{2}{3}R_0$. Тогда $R = R' + R_0 = \frac{2}{3}R_0 + R_0 = \frac{5}{3}R_0$.
Ответ: $\frac{5}{3}R_0$.
Также возможно собрать схему "мост", где все четыре резистора одинаковы. Такое соединение будет иметь эквивалентное сопротивление $R=R_0$, что не является новым значением.
Соберем все полученные уникальные значения сопротивлений (в долях от $R_0$):
$\frac{1}{4}, \frac{1}{3}, \frac{2}{5}, \frac{1}{2}, \frac{3}{5}, \frac{2}{3}, \frac{3}{4}, 1, \frac{4}{3}, \frac{3}{2}, \frac{5}{3}, 2, \frac{5}{2}, 3, 4$.
Другие задания:
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