gdz.top
Номер 26.1, страница 188 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Электродинамика. Постоянный электрический ток. 26. Электрический ток. Закон Ома для участка цепи - номер 26.1, страница 188.
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" => 1319695 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "188" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/26-1" "field_display_title" => "26.1" "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 {#1074 #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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "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" => 5400 "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 #items: array:1 [ 0 => App\Models\Term {#1042 #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" …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_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:2 [ 0 => App\Models\Term {#1044 #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 {#1045 #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 {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #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 {#1048 #items: array:3 [ 0 => App\Models\Term {#1049 #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 {#1050 #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 {#1051 #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 {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #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 {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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 {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 #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 {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ 0 => App\Models\Term {#1062 #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "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} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #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 {#1071 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "163" "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 {#1071} ] #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 {#1214 #items: array:3 [ 0 => App\Models\Branch {#1224 #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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1225 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "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 {#1259 #items: array:1 [ 0 => App\Models\Book {#1226 #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" => 5400 "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 {#1228 #items: array:1 [ 0 => App\Models\Term {#1227 #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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "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 {#1229 #items: array:2 [ 0 => App\Models\Term {#1230 #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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "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 => "*" ] } 1 => App\Models\Term {#1231 #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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "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 {#1232 #items: array:1 [ 0 => App\Models\Term {#1233 #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 {#1234 #items: array:3 [ 0 => App\Models\Term {#1235 #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 {#1236 #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 {#1237 #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 {#1238 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Term {#1240 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "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 {#1241 #items: array:1 [ 0 => App\Models\Term {#1242 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1243 #items: array:1 [ 0 => App\Models\Term {#1244 #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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "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 {#1245 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1246 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Term {#1248 #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" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1249 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1250 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1251 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1252 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1253 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1254 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ 0 => App\Models\Term {#1256 #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" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "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 {#1228} "field_class" => Illuminate\Database\Eloquent\Collection {#1229} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1232} "field_author" => Illuminate\Database\Eloquent\Collection {#1234} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1238} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1239} "field_country" => Illuminate\Database\Eloquent\Collection {#1241} "field_city" => Illuminate\Database\Eloquent\Collection {#1243} "field_series" => Illuminate\Database\Eloquent\Collection {#1245} "field_umk" => Illuminate\Database\Eloquent\Collection {#1246} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1247} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1249} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1250} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1251} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1252} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1253} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1254} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1255} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #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 {#1257 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1225} "field_page_start" => "163" "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 {#1259} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1257} ] #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 {#1258 #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" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1260 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "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 {#1261 #items: array:1 [ 0 => App\Models\Book {#1226} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1260} "field_page_start" => "188" "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 {#1261} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1262} ] #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 {#1263 #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" => 1319351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "26. Электрический ток. Закон Ома для участка цепи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1264 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "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 {#1265 #items: array:1 [ 0 => App\Models\Book {#1226} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:1 [ 0 => App\Models\Branch {#1273 #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" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1275 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "188" "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 {#1276 #items: array:1 [ 0 => App\Models\Book {#1226} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1275} "field_page_start" => "188" "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 {#1276} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1277} ] #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" => 1319351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "26. Электрический ток. Закон Ома для участка цепи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1264} "field_page_start" => "188" "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 {#1265} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1274} ] #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 {#1108 #items: array:2 [ 0 => App\Models\Element {#1211 #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" => 1493873 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ 0 => App\Models\Edition {#1209 #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" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:1 [ 0 => App\Models\Term {#1208 #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_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 {#1206 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1205 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1204 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1207} "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 {#1206} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1205} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1204} "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" => "1319695" "type" => "task" ] "text" => "<p><strong>26.1.</strong> Для измерения сопротивления проводника $\text{R}$ 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><em>Рис. а</em></p><p><em>Рис. б</em></p><p><strong>Решение.</strong> В схеме а амперметр дает правильные показания — он измеряет силу тока через резистор. А вот вольтметр «лжет»: он измеряет сумму напряжений на резисторе ($U_R$) и амперметре ($U_A$). Поэтому на самом деле $R = \frac{U_R}{I} = \frac{U - U_A}{I} = \frac{U}{I} - R_A$. Измерение по схеме а с использованием указанной в условии приближенной формулы дает малую погрешность для больших сопротивлений $R \gg R_A$ (сопротивление вольтметра при этом несущественно).</p><p>Рассматривая аналогично схему б, получаем $ \frac{1}{R} = \frac{I_R}{U} = \frac{I - I_V}{U} = \frac{I}{U} - \frac{1}{R_V} $. Погрешность в таком случае мала для малых сопротивлений $R \ll R_V$ (сопротивление амперметра при этом несущественно).</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1424" "height" => 1917 "path" => "/media/fizika_10/gelfgat-z/0-26/1-1.webp?ts=1756251100" ] ] ] #original: array:7 [ "id" => 1493873 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1201} "task" => array:2 [ "refs" => "1319695" "type" => "task" ] "text" => "<p><strong>26.1.</strong> Для измерения сопротивления проводника $\text{R}$ 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><em>Рис. а</em></p><p><em>Рис. б</em></p><p><strong>Решение.</strong> В схеме а амперметр дает правильные показания — он измеряет силу тока через резистор. А вот вольтметр «лжет»: он измеряет сумму напряжений на резисторе ($U_R$) и амперметре ($U_A$). Поэтому на самом деле $R = \frac{U_R}{I} = \frac{U - U_A}{I} = \frac{U}{I} - R_A$. Измерение по схеме а с использованием указанной в условии приближенной формулы дает малую погрешность для больших сопротивлений $R \gg R_A$ (сопротивление вольтметра при этом несущественно).</p><p>Рассматривая аналогично схему б, получаем $ \frac{1}{R} = \frac{I_R}{U} = \frac{I - I_V}{U} = \frac{I}{U} - \frac{1}{R_V} $. Погрешность в таком случае мала для малых сопротивлений $R \ll R_V$ (сопротивление амперметра при этом несущественно).</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1424" "height" => 1917 "path" => "/media/fizika_10/gelfgat-z/0-26/1-1.webp?ts=1756251100" ] ] ] #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 {#1202 #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" => 1691430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1193 #items: array:1 [ 0 => App\Models\Edition {#1203 #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" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198 #items: array:1 [ 0 => App\Models\Term {#1200 #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_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" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1199 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1196 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1197 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1198} "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" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1199} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1196} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1197} "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" => "1319695" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для анализа обеих схем введем обозначения: $R$ — искомое сопротивление, $R_A$ — сопротивление амперметра, $R_V$ — сопротивление вольтметра. $U$ и $I$ — показания вольтметра и амперметра соответственно.</p><p>Приближенная формула для расчета сопротивления: $R_{изм} = U/I$.</p><p><strong>Анализ схемы <em>а</em></strong></p><p>В схеме <em>а</em> амперметр включен последовательно с резистором $R$, поэтому он измеряет ток $I$, действительно протекающий через резистор. Вольтметр подключен параллельно последовательной цепи из резистора $R$ и амперметра. Таким образом, он измеряет суммарное падение напряжения на резисторе ($U_R$) и амперметре ($U_A$):</p><p>$U = U_R + U_A$</p><p>Истинное сопротивление $R$ определяется как $R = U_R / I$. Измеренное значение $R_{изм,а} = U / I$.</p><p>Подставим выражение для $U$:</p><p>$R_{изм,а} = (U_R + U_A) / I = U_R / I + U_A / I = R + R_A$</p><p>Таким образом, измеренное значение сопротивления больше истинного на величину сопротивления амперметра. Абсолютная погрешность равна $\Delta R_a = R_A$, а относительная погрешность: $\epsilon_a = \Delta R_a / R = R_A / R$.</p><p>Погрешность будет мала, если $R_A / R \ll 1$, то есть когда $R \gg R_A$.</p><p><strong>Анализ схемы <em>б</em></strong></p><p>В схеме <em>б</em> вольтметр подключен параллельно резистору $R$, поэтому он измеряет истинное напряжение на резисторе: $U = U_R$. Амперметр же включен до разветвления цепи и измеряет общий ток $I$, который равен сумме тока через резистор ($I_R$) и тока через вольтметр ($I_V$):</p><p>$I = I_R + I_V$</p><p>Истинное сопротивление $R = U / I_R$. Измеренное значение $R_{изм,б} = U / I$.</p><p>Подставим выражение для $I$:</p><p>$R_{изм,б} = U / (I_R + I_V)$</p><p>Выразим токи через напряжения и сопротивления, учитывая, что $I_R = U/R$ и $I_V = U/R_V$:</p><p>$R_{изм,б} = U / (U/R + U/R_V) = 1 / (1/R + 1/R_V)$</p><p>Отсюда видно, что измеренное сопротивление $R_{изм,б}$ является эквивалентным сопротивлением параллельно соединенных резистора $R$ и вольтметра $R_V$. Оно всегда меньше истинного сопротивления $R$.</p><p>Относительная погрешность: $\epsilon_б = |R_{изм,б} - R| / R = |(1 / (1/R + 1/R_V)) - R| / R = |(R R_V / (R + R_V)) - R| / R = |-R^2 / (R(R + R_V))| = R / (R + R_V)$.</p><p>Погрешность будет мала, если $R / (R + R_V) \ll 1$, то есть когда $R \ll R_V$.</p><p><strong>Какая из схем дает меньшую погрешность при измерении больших сопротивлений?</strong></p><p>При измерении больших сопротивлений ($R$ велико) сравним относительные погрешности:</p><ul><li>Схема <em>а</em>: $\epsilon_a = R_A / R$. С ростом $R$ погрешность $\epsilon_a$ уменьшается.</li><li>Схема <em>б</em>: $\epsilon_б = R / (R + R_V) = 1 / (1 + R_V/R)$. С ростом $R$ дробь $R_V/R$ стремится к нулю, а погрешность $\epsilon_б$ стремится к 1 (или 100%).</li></ul><p>Следовательно, для измерения больших сопротивлений (в идеале, когда $R \gg R_A$) меньшую погрешность дает схема <em>а</em>.</p><p><strong>Ответ:</strong> При измерении больших сопротивлений меньшую погрешность дает схема <em>а</em>.</p><p><strong>Малых сопротивлений?</strong></p><p>При измерении малых сопротивлений ($R$ мало) сравним относительные погрешности:</p><ul><li>Схема <em>а</em>: $\epsilon_a = R_A / R$. С уменьшением $R$ погрешность $\epsilon_a$ растет.</li><li>Схема <em>б</em>: $\epsilon_б = R / (R + R_V)$. С уменьшением $R$ погрешность $\epsilon_б$ также уменьшается.</li></ul><p>Следовательно, для измерения малых сопротивлений (в идеале, когда $R \ll R_V$) меньшую погрешность дает схема <em>б</em>.</p><p><strong>Ответ:</strong> При измерении малых сопротивлений меньшую погрешность дает схема <em>б</em>.</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>Чтобы найти точное значение $R$, нужно использовать формулы, учитывающие сопротивления измерительных приборов.</p><p>Для схемы <em>а</em> мы получили: $U/I = R + R_A$. Отсюда точная формула для $R$:</p><p>$R = U/I - R_A$</p><p>Для схемы <em>б</em> мы получили: $1 / (U/I) = 1/R + 1/R_V$. Отсюда $I/U = 1/R + 1/R_V$. Выразим $1/R$:</p><p>$1/R = I/U - 1/R_V$</p><p>Приведя к общему знаменателю и перевернув дробь, получим точную формулу для $R$:</p><p>$R = (U \cdot R_V) / (I \cdot R_V - U)$</p><p><strong>Ответ:</strong> Для схемы <em>а</em> точная формула: $R = U/I - R_A$. Для схемы <em>б</em> точная формула: $1/R = I/U - 1/R_V$ или $R = (U \cdot R_V) / (I \cdot R_V - U)$.</p>" ] #original: array:6 [ "id" => 1691430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1193} "task" => array:2 [ "refs" => "1319695" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для анализа обеих схем введем обозначения: $R$ — искомое сопротивление, $R_A$ — сопротивление амперметра, $R_V$ — сопротивление вольтметра. $U$ и $I$ — показания вольтметра и амперметра соответственно.</p><p>Приближенная формула для расчета сопротивления: $R_{изм} = U/I$.</p><p><strong>Анализ схемы <em>а</em></strong></p><p>В схеме <em>а</em> амперметр включен последовательно с резистором $R$, поэтому он измеряет ток $I$, действительно протекающий через резистор. Вольтметр подключен параллельно последовательной цепи из резистора $R$ и амперметра. Таким образом, он измеряет суммарное падение напряжения на резисторе ($U_R$) и амперметре ($U_A$):</p><p>$U = U_R + U_A$</p><p>Истинное сопротивление $R$ определяется как $R = U_R / I$. Измеренное значение $R_{изм,а} = U / I$.</p><p>Подставим выражение для $U$:</p><p>$R_{изм,а} = (U_R + U_A) / I = U_R / I + U_A / I = R + R_A$</p><p>Таким образом, измеренное значение сопротивления больше истинного на величину сопротивления амперметра. Абсолютная погрешность равна $\Delta R_a = R_A$, а относительная погрешность: $\epsilon_a = \Delta R_a / R = R_A / R$.</p><p>Погрешность будет мала, если $R_A / R \ll 1$, то есть когда $R \gg R_A$.</p><p><strong>Анализ схемы <em>б</em></strong></p><p>В схеме <em>б</em> вольтметр подключен параллельно резистору $R$, поэтому он измеряет истинное напряжение на резисторе: $U = U_R$. Амперметр же включен до разветвления цепи и измеряет общий ток $I$, который равен сумме тока через резистор ($I_R$) и тока через вольтметр ($I_V$):</p><p>$I = I_R + I_V$</p><p>Истинное сопротивление $R = U / I_R$. Измеренное значение $R_{изм,б} = U / I$.</p><p>Подставим выражение для $I$:</p><p>$R_{изм,б} = U / (I_R + I_V)$</p><p>Выразим токи через напряжения и сопротивления, учитывая, что $I_R = U/R$ и $I_V = U/R_V$:</p><p>$R_{изм,б} = U / (U/R + U/R_V) = 1 / (1/R + 1/R_V)$</p><p>Отсюда видно, что измеренное сопротивление $R_{изм,б}$ является эквивалентным сопротивлением параллельно соединенных резистора $R$ и вольтметра $R_V$. Оно всегда меньше истинного сопротивления $R$.</p><p>Относительная погрешность: $\epsilon_б = |R_{изм,б} - R| / R = |(1 / (1/R + 1/R_V)) - R| / R = |(R R_V / (R + R_V)) - R| / R = |-R^2 / (R(R + R_V))| = R / (R + R_V)$.</p><p>Погрешность будет мала, если $R / (R + R_V) \ll 1$, то есть когда $R \ll R_V$.</p><p><strong>Какая из схем дает меньшую погрешность при измерении больших сопротивлений?</strong></p><p>При измерении больших сопротивлений ($R$ велико) сравним относительные погрешности:</p><ul><li>Схема <em>а</em>: $\epsilon_a = R_A / R$. С ростом $R$ погрешность $\epsilon_a$ уменьшается.</li><li>Схема <em>б</em>: $\epsilon_б = R / (R + R_V) = 1 / (1 + R_V/R)$. С ростом $R$ дробь $R_V/R$ стремится к нулю, а погрешность $\epsilon_б$ стремится к 1 (или 100%).</li></ul><p>Следовательно, для измерения больших сопротивлений (в идеале, когда $R \gg R_A$) меньшую погрешность дает схема <em>а</em>.</p><p><strong>Ответ:</strong> При измерении больших сопротивлений меньшую погрешность дает схема <em>а</em>.</p><p><strong>Малых сопротивлений?</strong></p><p>При измерении малых сопротивлений ($R$ мало) сравним относительные погрешности:</p><ul><li>Схема <em>а</em>: $\epsilon_a = R_A / R$. С уменьшением $R$ погрешность $\epsilon_a$ растет.</li><li>Схема <em>б</em>: $\epsilon_б = R / (R + R_V)$. С уменьшением $R$ погрешность $\epsilon_б$ также уменьшается.</li></ul><p>Следовательно, для измерения малых сопротивлений (в идеале, когда $R \ll R_V$) меньшую погрешность дает схема <em>б</em>.</p><p><strong>Ответ:</strong> При измерении малых сопротивлений меньшую погрешность дает схема <em>б</em>.</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>Чтобы найти точное значение $R$, нужно использовать формулы, учитывающие сопротивления измерительных приборов.</p><p>Для схемы <em>а</em> мы получили: $U/I = R + R_A$. Отсюда точная формула для $R$:</p><p>$R = U/I - R_A$</p><p>Для схемы <em>б</em> мы получили: $1 / (U/I) = 1/R + 1/R_V$. Отсюда $I/U = 1/R + 1/R_V$. Выразим $1/R$:</p><p>$1/R = I/U - 1/R_V$</p><p>Приведя к общему знаменателю и перевернув дробь, получим точную формулу для $R$:</p><p>$R = (U \cdot R_V) / (I \cdot R_V - U)$</p><p><strong>Ответ:</strong> Для схемы <em>а</em> точная формула: $R = U/I - R_A$. Для схемы <em>б</em> точная формула: $1/R = I/U - 1/R_V$ или $R = (U \cdot R_V) / (I \cdot R_V - U)$.</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" => "1319696" "type" => "task" ] "previous" => array:2 [ "refs" => "1319694" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\Book {#1226} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\BookPage {#1212 #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" => 1341149 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "188" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-188" "field_display_title" => "188" "field_folder" => "1" "field_image_name" => "188" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1194 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1226} ] #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 {#1189 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Element {#1182 #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" => 1519694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1179 #items: array:1 [ 0 => App\Models\Edition {#1209} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341149" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "188-1.jpg" "alt" => null "width" => "1619" "height" => 2467 "path" => "/media/fizika_10/gelfgat-z/0-1/188-1.webp?ts=1756642376" ] ] ] #original: array:6 [ "id" => 1519694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1179} "book_page" => array:2 [ "refs" => "1341149" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "188-1.jpg" "alt" => null "width" => "1619" "height" => 2467 "path" => "/media/fizika_10/gelfgat-z/0-1/188-1.webp?ts=1756642376" ] ] ] #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" => "1341150" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341148" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Task {#1030} ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341149 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "188" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-188" "field_display_title" => "188" "field_folder" => "1" "field_image_name" => "188" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1194} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1195} "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 {#1189} "content" => Illuminate\Database\Eloquent\Collection {#1183} "next" => array:2 [ "refs" => "1341150" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341148" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1191} ] #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" => 1319695 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "188" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/26-1" "field_display_title" => "26.1" "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 {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1214} "content" => Illuminate\Database\Eloquent\Collection {#1108} "next" => array:2 [ "refs" => "1319696" "type" => "task" ] "previous" => array:2 [ "refs" => "1319694" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1180} "page" => array:2 [ "refs" => "1341149" "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 => "*" ] }
№26.1 (с. 188)
Условие. №26.1 (с. 188)
скриншот условия
26.1. Для измерения сопротивления проводника $\text{R}$ 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. В схеме а амперметр дает правильные показания — он измеряет силу тока через резистор. А вот вольтметр «лжет»: он измеряет сумму напряжений на резисторе ($U_R$) и амперметре ($U_A$). Поэтому на самом деле $R = \frac{U_R}{I} = \frac{U - U_A}{I} = \frac{U}{I} - R_A$. Измерение по схеме а с использованием указанной в условии приближенной формулы дает малую погрешность для больших сопротивлений $R \gg R_A$ (сопротивление вольтметра при этом несущественно).
Рассматривая аналогично схему б, получаем $ \frac{1}{R} = \frac{I_R}{U} = \frac{I - I_V}{U} = \frac{I}{U} - \frac{1}{R_V} $. Погрешность в таком случае мала для малых сопротивлений $R \ll R_V$ (сопротивление амперметра при этом несущественно).
Решение. №26.1 (с. 188)
Решение
Для анализа обеих схем введем обозначения: $R$ — искомое сопротивление, $R_A$ — сопротивление амперметра, $R_V$ — сопротивление вольтметра. $U$ и $I$ — показания вольтметра и амперметра соответственно.
Приближенная формула для расчета сопротивления: $R_{изм} = U/I$.
Анализ схемы а
В схеме а амперметр включен последовательно с резистором $R$, поэтому он измеряет ток $I$, действительно протекающий через резистор. Вольтметр подключен параллельно последовательной цепи из резистора $R$ и амперметра. Таким образом, он измеряет суммарное падение напряжения на резисторе ($U_R$) и амперметре ($U_A$):
$U = U_R + U_A$
Истинное сопротивление $R$ определяется как $R = U_R / I$. Измеренное значение $R_{изм,а} = U / I$.
Подставим выражение для $U$:
$R_{изм,а} = (U_R + U_A) / I = U_R / I + U_A / I = R + R_A$
Таким образом, измеренное значение сопротивления больше истинного на величину сопротивления амперметра. Абсолютная погрешность равна $\Delta R_a = R_A$, а относительная погрешность: $\epsilon_a = \Delta R_a / R = R_A / R$.
Погрешность будет мала, если $R_A / R \ll 1$, то есть когда $R \gg R_A$.
Анализ схемы б
В схеме б вольтметр подключен параллельно резистору $R$, поэтому он измеряет истинное напряжение на резисторе: $U = U_R$. Амперметр же включен до разветвления цепи и измеряет общий ток $I$, который равен сумме тока через резистор ($I_R$) и тока через вольтметр ($I_V$):
$I = I_R + I_V$
Истинное сопротивление $R = U / I_R$. Измеренное значение $R_{изм,б} = U / I$.
Подставим выражение для $I$:
$R_{изм,б} = U / (I_R + I_V)$
Выразим токи через напряжения и сопротивления, учитывая, что $I_R = U/R$ и $I_V = U/R_V$:
$R_{изм,б} = U / (U/R + U/R_V) = 1 / (1/R + 1/R_V)$
Отсюда видно, что измеренное сопротивление $R_{изм,б}$ является эквивалентным сопротивлением параллельно соединенных резистора $R$ и вольтметра $R_V$. Оно всегда меньше истинного сопротивления $R$.
Относительная погрешность: $\epsilon_б = |R_{изм,б} - R| / R = |(1 / (1/R + 1/R_V)) - R| / R = |(R R_V / (R + R_V)) - R| / R = |-R^2 / (R(R + R_V))| = R / (R + R_V)$.
Погрешность будет мала, если $R / (R + R_V) \ll 1$, то есть когда $R \ll R_V$.
Какая из схем дает меньшую погрешность при измерении больших сопротивлений?
При измерении больших сопротивлений ($R$ велико) сравним относительные погрешности:
- Схема а: $\epsilon_a = R_A / R$. С ростом $R$ погрешность $\epsilon_a$ уменьшается.
- Схема б: $\epsilon_б = R / (R + R_V) = 1 / (1 + R_V/R)$. С ростом $R$ дробь $R_V/R$ стремится к нулю, а погрешность $\epsilon_б$ стремится к 1 (или 100%).
Следовательно, для измерения больших сопротивлений (в идеале, когда $R \gg R_A$) меньшую погрешность дает схема а.
Ответ: При измерении больших сопротивлений меньшую погрешность дает схема а.
Малых сопротивлений?
При измерении малых сопротивлений ($R$ мало) сравним относительные погрешности:
- Схема а: $\epsilon_a = R_A / R$. С уменьшением $R$ погрешность $\epsilon_a$ растет.
- Схема б: $\epsilon_б = R / (R + R_V)$. С уменьшением $R$ погрешность $\epsilon_б$ также уменьшается.
Следовательно, для измерения малых сопротивлений (в идеале, когда $R \ll R_V$) меньшую погрешность дает схема 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.
Чтобы найти точное значение $R$, нужно использовать формулы, учитывающие сопротивления измерительных приборов.
Для схемы а мы получили: $U/I = R + R_A$. Отсюда точная формула для $R$:
$R = U/I - R_A$
Для схемы б мы получили: $1 / (U/I) = 1/R + 1/R_V$. Отсюда $I/U = 1/R + 1/R_V$. Выразим $1/R$:
$1/R = I/U - 1/R_V$
Приведя к общему знаменателю и перевернув дробь, получим точную формулу для $R$:
$R = (U \cdot R_V) / (I \cdot R_V - U)$
Ответ: Для схемы а точная формула: $R = U/I - R_A$. Для схемы б точная формула: $1/R = I/U - 1/R_V$ или $R = (U \cdot R_V) / (I \cdot R_V - U)$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 26.1 расположенного на странице 188 к задачнику 2008 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №26.1 (с. 188), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.