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Номер 13.3, страница 79 - 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 13.3, страница 79.
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" => 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 {#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 {#1298 #items: array:3 [ 0 => App\Models\Branch {#1074 #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 {#1077 #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 {#1075 #items: array:1 [ 0 => App\Models\Book {#1078 #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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …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 {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …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 {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …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 {#1111 #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 {#1077} "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 {#1075} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111} ] #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 {#1112 #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 {#1113 #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 {#1114 #items: array:1 [ 0 => App\Models\Book {#1115 #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 {#1116 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …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 {#1116 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …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 {#1148 #items: array:1 [ 0 => App\Models\Branch {#1149 #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 {#1150 …2} "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 {#1151 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1185 …2} ] #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 {#1150 …2} "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 {#1151 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1185 …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" => 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 {#1113} "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 {#1114} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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 {#1186 #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 {#1187 #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 {#1188 #items: array:1 [ 0 => App\Models\Book {#1189 #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 {#1190 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1216 …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 {#1217 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1220 …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 {#1190 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1216 …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 {#1217 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1220 …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 {#1222 #items: array:1 [ 0 => App\Models\Branch {#1223 #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 {#1224 …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 {#1225 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1259 …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 {#1224 …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 {#1225 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1259 …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 {#1187} "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 {#1188} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1222} ] #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 {#1315 #items: array:3 [ 0 => App\Models\Element {#1325 #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" => 1478530 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1334 #items: array:1 [ 0 => App\Models\Edition {#1326 #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 {#1328 …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 {#1329 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1330 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1331 …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 {#1328 …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 {#1329 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1330 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1331 …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" => "1288454" "type" => "task" ] "text" => "<p><strong>13.3.</strong> Для измерения сопротивления проводника R используют одну из двух схем (рис. а, б). Сопротивление проводника вычисляют по приближенной формуле $R = U/I$, где $\text{U}$ — показание вольтметра, $\text{I}$ — показание амперметра. Какая из схем дает меньшую погрешность при измерении больших сопротивлений? Малых сопротивлений? Выведите формулы, позволяющие с помощью этих схем измерить $\text{R}$ как можно более точно, зная сопротивления амперметра $R_A$ и вольтметра $R_V$.</p><p>Рис. а</p><p>Рис. б</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1444" "height" => 574 "path" => "/media/fizika_08/gelfgat-u/0-13/3-1.webp?ts=1756049943" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1409" "height" => 385 "path" => "/media/fizika_08/gelfgat-u/0-13/3-2.webp?ts=1756049943" ] ] ] #original: array:7 [ "id" => 1478530 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1334} "task" => array:2 [ "refs" => "1288454" "type" => "task" ] "text" => "<p><strong>13.3.</strong> Для измерения сопротивления проводника R используют одну из двух схем (рис. а, б). Сопротивление проводника вычисляют по приближенной формуле $R = U/I$, где $\text{U}$ — показание вольтметра, $\text{I}$ — показание амперметра. Какая из схем дает меньшую погрешность при измерении больших сопротивлений? Малых сопротивлений? Выведите формулы, позволяющие с помощью этих схем измерить $\text{R}$ как можно более точно, зная сопротивления амперметра $R_A$ и вольтметра $R_V$.</p><p>Рис. а</p><p>Рис. б</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1444" "height" => 574 "path" => "/media/fizika_08/gelfgat-u/0-13/3-1.webp?ts=1756049943" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1409" "height" => 385 "path" => "/media/fizika_08/gelfgat-u/0-13/3-2.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 {#1332 #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" => 1479018 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1342 #items: array:1 [ 0 => App\Models\Edition {#1333 #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 {#1336 …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 {#1337 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1338 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1339 …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 {#1336 …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 {#1337 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1338 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1339 …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" => "1288454" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1411" "height" => 644 "path" => "/media/fizika_08/gelfgat-u/1-13/3-1.webp?ts=1756050016" ] ] ] #original: array:6 [ "id" => 1479018 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1342} "task" => array:2 [ "refs" => "1288454" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1411" "height" => 644 "path" => "/media/fizika_08/gelfgat-u/1-13/3-1.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 {#1340 #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" => 1738147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1350 #items: array:1 [ 0 => App\Models\Edition {#1341 #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 {#1344 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null …11 ] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1288454" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Две схемы для измерения сопротивления R (рис. а, рис. б).</p><p>Сопротивление амперметра: $R_A$.</p><p>Сопротивление вольтметра: $R_V$.</p><p>Показания приборов: $\text{U}$ (вольтметр), $\text{I}$ (амперметр).</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Схему с меньшей погрешностью для измерения больших R.</p><p><strong>2.</strong> Схему с меньшей погрешностью для измерения малых R.</p><p><strong>3.</strong> Точные формулы для R для каждой схемы.</p><p><strong>Решение:</strong></p><p>Для определения погрешностей, вносимых измерительными приборами, проанализируем каждую схему.</p><p><strong>Анализ схемы а (Рис. а)</strong></p><p>В этой схеме амперметр включен последовательно с резистором R. Он показывает истинный ток $\text{I}$, протекающий через резистор. Вольтметр, включенный параллельно связке из резистора и амперметра, измеряет суммарное падение напряжения на них:</p><p>$U = U_R + U_A = I \cdot R + I \cdot R_A = I(R + R_A)$</p><p>Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:</p><p>$R_{изм,а} = \frac{I(R + R_A)}{I} = R + R_A$</p><p>Измеренное значение оказывается больше истинного на величину сопротивления амперметра. Относительная погрешность измерения составляет:</p><p>$\epsilon_a = \frac{R_{изм,а} - R}{R} = \frac{(R + R_A) - R}{R} = \frac{R_A}{R}$</p><p><strong>Анализ схемы б (Рис. б)</strong></p><p>В этой схеме вольтметр подключен параллельно резистору R и измеряет истинное напряжение $\text{U}$ на нем. Амперметр измеряет общий ток $\text{I}$, который разветвляется на ток через резистор ($I_R$) и ток через вольтметр ($I_V$).</p><p>$I = I_R + I_V$</p><p>Используя закон Ома, найдем токи:</p><p>$I_R = \frac{U}{R}$, $I_V = \frac{U}{R_V}$</p><p>Показание амперметра: $I = \frac{U}{R} + \frac{U}{R_V} = U(\frac{1}{R} + \frac{1}{R_V})$</p><p>Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:</p><p>$R_{изм,б} = \frac{U}{U(\frac{1}{R} + \frac{1}{R_V})} = \frac{1}{\frac{1}{R} + \frac{1}{R_V}} = \frac{R \cdot R_V}{R + R_V}$</p><p>Измеренное значение меньше истинного и равно эквивалентному сопротивлению параллельно соединенных резистора R и вольтметра. Относительная погрешность измерения (по модулю) составляет:</p><p>$\epsilon_б = \frac{|R_{изм,б} - R|}{R} = \frac{| \frac{R \cdot R_V}{R + R_V} - R |}{R} = \frac{| \frac{-R^2}{R+R_V} |}{R} = \frac{R}{R+R_V}$</p><p>Теперь, основываясь на полученных формулах для погрешностей, ответим на вопросы задачи.</p><p><strong>Какая из схем дает меньшую погрешность при измерении больших сопротивлений?</strong></p><p>При измерении больших сопротивлений (R велико) относительная погрешность для схемы <strong>а</strong>, равная $\epsilon_a = R_A/R$, становится очень малой, поскольку сопротивление идеального амперметра $R_A$ стремится к нулю. В то же время, для схемы <strong>б</strong> погрешность $\epsilon_б = R/(R+R_V) = 1/(1 + R_V/R)$ стремится к 1 (т.е. к 100%), так как сопротивление идеального вольтметра $R_V$ конечно, и при $R \rightarrow \infty$ дробь $R_V/R \rightarrow 0$. Таким образом, для измерения больших сопротивлений предпочтительнее использовать схему <strong>а</strong>.</p><p><strong>Ответ:</strong> При измерении больших сопротивлений меньшую погрешность дает схема <strong>а</strong>.</p><p><strong>Какая из схем дает меньшую погрешность при измерении малых сопротивлений?</strong></p><p>При измерении малых сопротивлений (R мало) относительная погрешность для схемы <strong>а</strong>, $\epsilon_a = R_A/R$, может быть значительной, если R сопоставимо с сопротивлением амперметра $R_A$. Для схемы <strong>б</strong> погрешность $\epsilon_б = R/(R+R_V)$ будет очень малой, так как сопротивление вольтметра $R_V$ очень велико (в идеале $R_V \rightarrow \infty$), и $R \ll R_V$. Следовательно, для измерения малых сопротивлений предпочтительнее использовать схему <strong>б</strong>.</p><p><strong>Ответ:</strong> При измерении малых сопротивлений меньшую погрешность дает схема <strong>б</strong>.</p><p><strong>Выведите формулы, позволяющие с помощью этих схем измерить R как можно более точно, зная сопротивления амперметра R<sub>A</sub> и вольтметра R<sub>V</sub>.</strong></p><p><em>Для схемы а:</em></p><p>Мы установили, что показания приборов $\text{U}$ и $\text{I}$ связаны с истинным сопротивлением $\text{R}$ соотношением $U = I(R + R_A)$. Выразим из этой формулы R:</p><p>$\frac{U}{I} = R + R_A$</p><p>$R = \frac{U}{I} - R_A$</p><p><em>Для схемы б:</em></p><p>Мы установили, что $I = U(\frac{1}{R} + \frac{1}{R_V})$. Выразим отсюда R:</p><p>$\frac{I}{U} = \frac{1}{R} + \frac{1}{R_V}$</p><p>$\frac{1}{R} = \frac{I}{U} - \frac{1}{R_V} = \frac{I \cdot R_V - U}{U \cdot R_V}$</p><p>$R = \frac{U \cdot R_V}{I \cdot R_V - U}$</p><p><strong>Ответ:</strong> Точная формула для схемы <strong>а</strong>: $R = \frac{U}{I} - R_A$. Точная формула для схемы <strong>б</strong>: $R = \frac{U \cdot R_V}{I \cdot R_V - U}$.</p>" ] #original: array:6 [ "id" => 1738147 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1350} "task" => array:2 [ "refs" => "1288454" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Две схемы для измерения сопротивления R (рис. а, рис. б).</p><p>Сопротивление амперметра: $R_A$.</p><p>Сопротивление вольтметра: $R_V$.</p><p>Показания приборов: $\text{U}$ (вольтметр), $\text{I}$ (амперметр).</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Схему с меньшей погрешностью для измерения больших R.</p><p><strong>2.</strong> Схему с меньшей погрешностью для измерения малых R.</p><p><strong>3.</strong> Точные формулы для R для каждой схемы.</p><p><strong>Решение:</strong></p><p>Для определения погрешностей, вносимых измерительными приборами, проанализируем каждую схему.</p><p><strong>Анализ схемы а (Рис. а)</strong></p><p>В этой схеме амперметр включен последовательно с резистором R. Он показывает истинный ток $\text{I}$, протекающий через резистор. Вольтметр, включенный параллельно связке из резистора и амперметра, измеряет суммарное падение напряжения на них:</p><p>$U = U_R + U_A = I \cdot R + I \cdot R_A = I(R + R_A)$</p><p>Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:</p><p>$R_{изм,а} = \frac{I(R + R_A)}{I} = R + R_A$</p><p>Измеренное значение оказывается больше истинного на величину сопротивления амперметра. Относительная погрешность измерения составляет:</p><p>$\epsilon_a = \frac{R_{изм,а} - R}{R} = \frac{(R + R_A) - R}{R} = \frac{R_A}{R}$</p><p><strong>Анализ схемы б (Рис. б)</strong></p><p>В этой схеме вольтметр подключен параллельно резистору R и измеряет истинное напряжение $\text{U}$ на нем. Амперметр измеряет общий ток $\text{I}$, который разветвляется на ток через резистор ($I_R$) и ток через вольтметр ($I_V$).</p><p>$I = I_R + I_V$</p><p>Используя закон Ома, найдем токи:</p><p>$I_R = \frac{U}{R}$, $I_V = \frac{U}{R_V}$</p><p>Показание амперметра: $I = \frac{U}{R} + \frac{U}{R_V} = U(\frac{1}{R} + \frac{1}{R_V})$</p><p>Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:</p><p>$R_{изм,б} = \frac{U}{U(\frac{1}{R} + \frac{1}{R_V})} = \frac{1}{\frac{1}{R} + \frac{1}{R_V}} = \frac{R \cdot R_V}{R + R_V}$</p><p>Измеренное значение меньше истинного и равно эквивалентному сопротивлению параллельно соединенных резистора R и вольтметра. Относительная погрешность измерения (по модулю) составляет:</p><p>$\epsilon_б = \frac{|R_{изм,б} - R|}{R} = \frac{| \frac{R \cdot R_V}{R + R_V} - R |}{R} = \frac{| \frac{-R^2}{R+R_V} |}{R} = \frac{R}{R+R_V}$</p><p>Теперь, основываясь на полученных формулах для погрешностей, ответим на вопросы задачи.</p><p><strong>Какая из схем дает меньшую погрешность при измерении больших сопротивлений?</strong></p><p>При измерении больших сопротивлений (R велико) относительная погрешность для схемы <strong>а</strong>, равная $\epsilon_a = R_A/R$, становится очень малой, поскольку сопротивление идеального амперметра $R_A$ стремится к нулю. В то же время, для схемы <strong>б</strong> погрешность $\epsilon_б = R/(R+R_V) = 1/(1 + R_V/R)$ стремится к 1 (т.е. к 100%), так как сопротивление идеального вольтметра $R_V$ конечно, и при $R \rightarrow \infty$ дробь $R_V/R \rightarrow 0$. Таким образом, для измерения больших сопротивлений предпочтительнее использовать схему <strong>а</strong>.</p><p><strong>Ответ:</strong> При измерении больших сопротивлений меньшую погрешность дает схема <strong>а</strong>.</p><p><strong>Какая из схем дает меньшую погрешность при измерении малых сопротивлений?</strong></p><p>При измерении малых сопротивлений (R мало) относительная погрешность для схемы <strong>а</strong>, $\epsilon_a = R_A/R$, может быть значительной, если R сопоставимо с сопротивлением амперметра $R_A$. Для схемы <strong>б</strong> погрешность $\epsilon_б = R/(R+R_V)$ будет очень малой, так как сопротивление вольтметра $R_V$ очень велико (в идеале $R_V \rightarrow \infty$), и $R \ll R_V$. Следовательно, для измерения малых сопротивлений предпочтительнее использовать схему <strong>б</strong>.</p><p><strong>Ответ:</strong> При измерении малых сопротивлений меньшую погрешность дает схема <strong>б</strong>.</p><p><strong>Выведите формулы, позволяющие с помощью этих схем измерить R как можно более точно, зная сопротивления амперметра R<sub>A</sub> и вольтметра R<sub>V</sub>.</strong></p><p><em>Для схемы а:</em></p><p>Мы установили, что показания приборов $\text{U}$ и $\text{I}$ связаны с истинным сопротивлением $\text{R}$ соотношением $U = I(R + R_A)$. Выразим из этой формулы R:</p><p>$\frac{U}{I} = R + R_A$</p><p>$R = \frac{U}{I} - R_A$</p><p><em>Для схемы б:</em></p><p>Мы установили, что $I = U(\frac{1}{R} + \frac{1}{R_V})$. Выразим отсюда R:</p><p>$\frac{I}{U} = \frac{1}{R} + \frac{1}{R_V}$</p><p>$\frac{1}{R} = \frac{I}{U} - \frac{1}{R_V} = \frac{I \cdot R_V - U}{U \cdot R_V}$</p><p>$R = \frac{U \cdot R_V}{I \cdot R_V - U}$</p><p><strong>Ответ:</strong> Точная формула для схемы <strong>а</strong>: $R = \frac{U}{I} - R_A$. Точная формула для схемы <strong>б</strong>: $R = \frac{U \cdot R_V}{I \cdot R_V - U}$.</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" => "1288455" "type" => "task" ] "previous" => array:2 [ "refs" => "1288453" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1359 #items: array:1 [ 0 => App\Models\Book {#1322 #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 {#1307 #items: array:1 [ 0 => App\Models\Term {#1306 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1308 #items: array:4 [ 0 => App\Models\Term {#1313 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1312 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1311 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Term {#1309 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1310 #items: array:1 [ 0 => App\Models\Term {#1299 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:3 [ 0 => App\Models\Term {#1297 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1305 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1304 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1303 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1301 #items: array:1 [ 0 => App\Models\Term {#1302 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1316 #items: array:1 [ 0 => App\Models\Term {#1314 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1321 #items: array:1 [ 0 => App\Models\Term {#1323 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1319 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1317 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1320 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1318 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1348 #items: array:1 [ 0 => App\Models\Term {#1349 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1351 #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 {#1352 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1353 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1354 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1355 #items: array:1 [ 0 => App\Models\Term {#1356 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 {#1307} "field_class" => Illuminate\Database\Eloquent\Collection {#1308} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1310} "field_author" => Illuminate\Database\Eloquent\Collection {#1300} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1303} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1301} "field_country" => Illuminate\Database\Eloquent\Collection {#1316} "field_city" => Illuminate\Database\Eloquent\Collection {#1321} "field_series" => Illuminate\Database\Eloquent\Collection {#1319} "field_umk" => Illuminate\Database\Eloquent\Collection {#1317} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1320} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1318} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1348} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1351} "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 {#1352} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1353} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1354} "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1355} "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 } "page" => Illuminate\Database\Eloquent\Collection {#1696 #items: array:1 [ 0 => App\Models\BookPage {#1032 #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" => 1340430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_url" => "/8-klass/fizika/ileksa-gelfgat-uchebnik/page-79" "field_display_title" => "79" "field_folder" => "1" "field_image_name" => "79" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Book {#1357 #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 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #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 {#1391 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1392 #items: array:1 [ 0 => App\Models\Element {#1393 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] 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#touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 3 => App\Models\Task {#1643 #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] } 4 => App\Models\Task {#1668 #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] 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№13.3 (с. 79)
Условие. №13.3 (с. 79)
скриншот условия
13.3. Для измерения сопротивления проводника R используют одну из двух схем (рис. а, б). Сопротивление проводника вычисляют по приближенной формуле $R = U/I$, где $\text{U}$ — показание вольтметра, $\text{I}$ — показание амперметра. Какая из схем дает меньшую погрешность при измерении больших сопротивлений? Малых сопротивлений? Выведите формулы, позволяющие с помощью этих схем измерить $\text{R}$ как можно более точно, зная сопротивления амперметра $R_A$ и вольтметра $R_V$.
Рис. а
Рис. б
Решение. №13.3 (с. 79)
Решение 2. №13.3 (с. 79)
Дано:
Две схемы для измерения сопротивления R (рис. а, рис. б).
Сопротивление амперметра: $R_A$.
Сопротивление вольтметра: $R_V$.
Показания приборов: $\text{U}$ (вольтметр), $\text{I}$ (амперметр).
Найти:
1. Схему с меньшей погрешностью для измерения больших R.
2. Схему с меньшей погрешностью для измерения малых R.
3. Точные формулы для R для каждой схемы.
Решение:
Для определения погрешностей, вносимых измерительными приборами, проанализируем каждую схему.
Анализ схемы а (Рис. а)
В этой схеме амперметр включен последовательно с резистором R. Он показывает истинный ток $\text{I}$, протекающий через резистор. Вольтметр, включенный параллельно связке из резистора и амперметра, измеряет суммарное падение напряжения на них:
$U = U_R + U_A = I \cdot R + I \cdot R_A = I(R + R_A)$
Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:
$R_{изм,а} = \frac{I(R + R_A)}{I} = R + R_A$
Измеренное значение оказывается больше истинного на величину сопротивления амперметра. Относительная погрешность измерения составляет:
$\epsilon_a = \frac{R_{изм,а} - R}{R} = \frac{(R + R_A) - R}{R} = \frac{R_A}{R}$
Анализ схемы б (Рис. б)
В этой схеме вольтметр подключен параллельно резистору R и измеряет истинное напряжение $\text{U}$ на нем. Амперметр измеряет общий ток $\text{I}$, который разветвляется на ток через резистор ($I_R$) и ток через вольтметр ($I_V$).
$I = I_R + I_V$
Используя закон Ома, найдем токи:
$I_R = \frac{U}{R}$, $I_V = \frac{U}{R_V}$
Показание амперметра: $I = \frac{U}{R} + \frac{U}{R_V} = U(\frac{1}{R} + \frac{1}{R_V})$
Сопротивление, вычисленное по приближенной формуле $R_{изм} = U/I$, будет равно:
$R_{изм,б} = \frac{U}{U(\frac{1}{R} + \frac{1}{R_V})} = \frac{1}{\frac{1}{R} + \frac{1}{R_V}} = \frac{R \cdot R_V}{R + R_V}$
Измеренное значение меньше истинного и равно эквивалентному сопротивлению параллельно соединенных резистора R и вольтметра. Относительная погрешность измерения (по модулю) составляет:
$\epsilon_б = \frac{|R_{изм,б} - R|}{R} = \frac{| \frac{R \cdot R_V}{R + R_V} - R |}{R} = \frac{| \frac{-R^2}{R+R_V} |}{R} = \frac{R}{R+R_V}$
Теперь, основываясь на полученных формулах для погрешностей, ответим на вопросы задачи.
Какая из схем дает меньшую погрешность при измерении больших сопротивлений?
При измерении больших сопротивлений (R велико) относительная погрешность для схемы а, равная $\epsilon_a = R_A/R$, становится очень малой, поскольку сопротивление идеального амперметра $R_A$ стремится к нулю. В то же время, для схемы б погрешность $\epsilon_б = R/(R+R_V) = 1/(1 + R_V/R)$ стремится к 1 (т.е. к 100%), так как сопротивление идеального вольтметра $R_V$ конечно, и при $R \rightarrow \infty$ дробь $R_V/R \rightarrow 0$. Таким образом, для измерения больших сопротивлений предпочтительнее использовать схему а.
Ответ: При измерении больших сопротивлений меньшую погрешность дает схема а.
Какая из схем дает меньшую погрешность при измерении малых сопротивлений?
При измерении малых сопротивлений (R мало) относительная погрешность для схемы а, $\epsilon_a = R_A/R$, может быть значительной, если R сопоставимо с сопротивлением амперметра $R_A$. Для схемы б погрешность $\epsilon_б = R/(R+R_V)$ будет очень малой, так как сопротивление вольтметра $R_V$ очень велико (в идеале $R_V \rightarrow \infty$), и $R \ll R_V$. Следовательно, для измерения малых сопротивлений предпочтительнее использовать схему б.
Ответ: При измерении малых сопротивлений меньшую погрешность дает схема б.
Выведите формулы, позволяющие с помощью этих схем измерить R как можно более точно, зная сопротивления амперметра RA и вольтметра RV.
Для схемы а:
Мы установили, что показания приборов $\text{U}$ и $\text{I}$ связаны с истинным сопротивлением $\text{R}$ соотношением $U = I(R + R_A)$. Выразим из этой формулы R:
$\frac{U}{I} = R + R_A$
$R = \frac{U}{I} - R_A$
Для схемы б:
Мы установили, что $I = U(\frac{1}{R} + \frac{1}{R_V})$. Выразим отсюда R:
$\frac{I}{U} = \frac{1}{R} + \frac{1}{R_V}$
$\frac{1}{R} = \frac{I}{U} - \frac{1}{R_V} = \frac{I \cdot R_V - U}{U \cdot R_V}$
$R = \frac{U \cdot R_V}{I \cdot R_V - U}$
Ответ: Точная формула для схемы а: $R = \frac{U}{I} - R_A$. Точная формула для схемы б: $R = \frac{U \cdot R_V}{I \cdot R_V - U}$.
Другие задания:
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