gdz.top
Номер 27.1, страница 190 - 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. 27. Последовательное и параллельное соединение проводников. Упражнения - номер 27.1, страница 190.
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" => 1319697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-1" "field_display_title" => "27.1" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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 {#1047 #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 {#1081 #items: array:1 [ 0 => App\Models\Book {#1048 #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 {#1050 #items: array:1 [ 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: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 {#1051 #items: array:2 [ 0 => App\Models\Term {#1052 #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 {#1053 #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 {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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 {#1056 #items: array:3 [ 0 => App\Models\Term {#1057 #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 {#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: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 {#1059 #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 {#1060 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: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 {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #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 {#1065 #items: array:1 [ 0 => App\Models\Term {#1066 #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 {#1067 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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 [ "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 {#1071 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073 #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 {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1060} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1061} "field_country" => Illuminate\Database\Eloquent\Collection {#1063} "field_city" => Illuminate\Database\Eloquent\Collection {#1065} "field_series" => Illuminate\Database\Eloquent\Collection {#1067} "field_umk" => Illuminate\Database\Eloquent\Collection {#1068} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "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 {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1079 #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 {#1047} "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 {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #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 {#1111 #items: array:4 [ 0 => App\Models\Branch {#1121 #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 {#1122 #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 {#1123 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124 #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 {#1122} "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 {#1123} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124} ] #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 {#1125 #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 {#1126 #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 {#1127 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #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 {#1126} "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 {#1127} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128} ] #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 {#1129 #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" => 1319352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "27. Последовательное и параллельное соединение проводников" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "190" "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 {#1131 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Branch {#1139 #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 {#1141 #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 {#1142 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #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 {#1141} "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 {#1142} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143} ] #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" => 1319352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "27. Последовательное и параллельное соединение проводников" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "190" "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 {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1140} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Branch {#1133 #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" => 1319353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "190" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149 #items: array:1 [ 0 => App\Models\Branch {#1148 #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" => 1319352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "27. Последовательное и параллельное соединение проводников" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "190" "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 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Branch {#1139} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "27. Последовательное и параллельное соединение проводников" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1150} "field_page_start" => "190" "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} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152} ] #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" => 1319353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "190" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1149} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1102 #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" => 1493875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1101 #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 {#1098 #items: array:1 [ 0 => App\Models\Term {#1100 #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_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 {#1099 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096 #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 {#1098} "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 {#1099} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1097} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1096} "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" => "1319697" "type" => "task" ] "text" => "<p><strong>27.1.</strong> Из проволоки сопротивлением $R_0 = 32 \text{ Ом}$ сделано кольцо. В каких точках кольца следует подключить провода, чтобы получить сопротивление $R = 6 \text{ Ом}$?</p><p>Точки подключения должны делить кольцо в отношении 1:3.</p><p><strong>Решение.</strong> Участки кольца соединены между собой параллельно. Обозначим длину кольца $\text{l}$, а длину одного из участков $\text{x}$. Тогда сопротивления участков $R_0x/l$ и $R_0(l-x)/l$, а сопротивление всей цепи $R = R_0x(l-x)/l^2$. Отсюда находим отношение $x/l$: оно равно 0,25 или 0,75. Оба значения соответствуют одному решению — делению кольца на две части в отношении 1:3.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1377" "height" => 757 "path" => "/media/fizika_10/gelfgat-z/0-27/1-1.webp?ts=1756251100" ] ] ] #original: array:7 [ "id" => 1493875 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1319697" "type" => "task" ] "text" => "<p><strong>27.1.</strong> Из проволоки сопротивлением $R_0 = 32 \text{ Ом}$ сделано кольцо. В каких точках кольца следует подключить провода, чтобы получить сопротивление $R = 6 \text{ Ом}$?</p><p>Точки подключения должны делить кольцо в отношении 1:3.</p><p><strong>Решение.</strong> Участки кольца соединены между собой параллельно. Обозначим длину кольца $\text{l}$, а длину одного из участков $\text{x}$. Тогда сопротивления участков $R_0x/l$ и $R_0(l-x)/l$, а сопротивление всей цепи $R = R_0x(l-x)/l^2$. Отсюда находим отношение $x/l$: оно равно 0,25 или 0,75. Оба значения соответствуют одному решению — делению кольца на две части в отношении 1:3.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1377" "height" => 757 "path" => "/media/fizika_10/gelfgat-z/0-27/1-1.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 {#1094 #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" => 1691432 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Edition {#1095 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Term {#1093 #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" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #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_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 {#1091 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1085 #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 {#1090} "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 {#1091} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1089} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1085} "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" => "1319697" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Сопротивление всей проволоки (кольца), $R_0 = 32$ Ом.</p><p>Требуемое общее сопротивление, $R = 6$ Ом.</p><p><strong>Найти:</strong></p><p>Отношение, в котором точки подключения должны делить длину кольца.</p><p><strong>Решение:</strong></p><p>При подключении проводов к двум точкам на кольце, оно разделяется на два участка (две дуги), которые оказываются соединенными параллельно. Обозначим сопротивления этих участков как $R_1$ и $R_2$.</p><p>Так как эти два участка вместе составляют исходную проволоку, сумма их сопротивлений равна общему сопротивлению проволоки:</p><p>$R_1 + R_2 = R_0 = 32$ Ом.</p><p>Общее сопротивление $R$ при параллельном соединении вычисляется по формуле:</p><p>$R = \frac{R_1 R_2}{R_1 + R_2}$</p><p>Подставим известные значения $R$ и $R_0$ в эту формулу:</p><p>$6 = \frac{R_1 R_2}{32}$</p><p>Из этого уравнения можно найти произведение сопротивлений $R_1$ и $R_2$:</p><p>$R_1 R_2 = 6 \cdot 32 = 192$ (Ом²)</p><p>Таким образом, мы имеем систему из двух уравнений:</p><p>1) $R_1 + R_2 = 32$</p><p>2) $R_1 R_2 = 192$</p><p>Это система уравнений, которую можно решить, например, методом подстановки. Выразим $R_2$ из первого уравнения: $R_2 = 32 - R_1$. Подставим это выражение во второе уравнение:</p><p>$R_1 (32 - R_1) = 192$</p><p>$32 R_1 - R_1^2 = 192$</p><p>Приведем уравнение к стандартному квадратному виду:</p><p>$R_1^2 - 32 R_1 + 192 = 0$</p><p>Решим это квадратное уравнение. Найдем дискриминант:</p><p>$D = b^2 - 4ac = (-32)^2 - 4 \cdot 1 \cdot 192 = 1024 - 768 = 256$</p><p>Найдем корни уравнения:</p><p>$R_1 = \frac{-b \pm \sqrt{D}}{2a} = \frac{32 \pm \sqrt{256}}{2} = \frac{32 \pm 16}{2}$</p><p>Получаем два возможных значения для $R_1$:</p><p>$R_{1,1} = \frac{32 + 16}{2} = \frac{48}{2} = 24$ Ом.</p><p>$R_{1,2} = \frac{32 - 16}{2} = \frac{16}{2} = 8$ Ом.</p><p>Если $R_1 = 24$ Ом, то $R_2 = 32 - 24 = 8$ Ом.</p><p>Если $R_1 = 8$ Ом, то $R_2 = 32 - 8 = 24$ Ом.</p><p>Оба случая описывают одну и ту же ситуацию: кольцо разделено на два участка с сопротивлениями 8 Ом и 24 Ом.</p><p>Для однородной проволоки сопротивление прямо пропорционально ее длине. Поэтому отношение длин участков будет равно отношению их сопротивлений:</p><p>$\frac{L_1}{L_2} = \frac{R_1}{R_2} = \frac{8}{24} = \frac{1}{3}$</p><p>Следовательно, провода нужно подключить так, чтобы они делили кольцо на части, длины которых относятся как 1 к 3.</p><p><strong>Ответ:</strong> Точки подключения должны делить кольцо в отношении 1:3.</p>" ] #original: array:6 [ "id" => 1691432 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1086} "task" => array:2 [ "refs" => "1319697" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Сопротивление всей проволоки (кольца), $R_0 = 32$ Ом.</p><p>Требуемое общее сопротивление, $R = 6$ Ом.</p><p><strong>Найти:</strong></p><p>Отношение, в котором точки подключения должны делить длину кольца.</p><p><strong>Решение:</strong></p><p>При подключении проводов к двум точкам на кольце, оно разделяется на два участка (две дуги), которые оказываются соединенными параллельно. Обозначим сопротивления этих участков как $R_1$ и $R_2$.</p><p>Так как эти два участка вместе составляют исходную проволоку, сумма их сопротивлений равна общему сопротивлению проволоки:</p><p>$R_1 + R_2 = R_0 = 32$ Ом.</p><p>Общее сопротивление $R$ при параллельном соединении вычисляется по формуле:</p><p>$R = \frac{R_1 R_2}{R_1 + R_2}$</p><p>Подставим известные значения $R$ и $R_0$ в эту формулу:</p><p>$6 = \frac{R_1 R_2}{32}$</p><p>Из этого уравнения можно найти произведение сопротивлений $R_1$ и $R_2$:</p><p>$R_1 R_2 = 6 \cdot 32 = 192$ (Ом²)</p><p>Таким образом, мы имеем систему из двух уравнений:</p><p>1) $R_1 + R_2 = 32$</p><p>2) $R_1 R_2 = 192$</p><p>Это система уравнений, которую можно решить, например, методом подстановки. Выразим $R_2$ из первого уравнения: $R_2 = 32 - R_1$. Подставим это выражение во второе уравнение:</p><p>$R_1 (32 - R_1) = 192$</p><p>$32 R_1 - R_1^2 = 192$</p><p>Приведем уравнение к стандартному квадратному виду:</p><p>$R_1^2 - 32 R_1 + 192 = 0$</p><p>Решим это квадратное уравнение. Найдем дискриминант:</p><p>$D = b^2 - 4ac = (-32)^2 - 4 \cdot 1 \cdot 192 = 1024 - 768 = 256$</p><p>Найдем корни уравнения:</p><p>$R_1 = \frac{-b \pm \sqrt{D}}{2a} = \frac{32 \pm \sqrt{256}}{2} = \frac{32 \pm 16}{2}$</p><p>Получаем два возможных значения для $R_1$:</p><p>$R_{1,1} = \frac{32 + 16}{2} = \frac{48}{2} = 24$ Ом.</p><p>$R_{1,2} = \frac{32 - 16}{2} = \frac{16}{2} = 8$ Ом.</p><p>Если $R_1 = 24$ Ом, то $R_2 = 32 - 24 = 8$ Ом.</p><p>Если $R_1 = 8$ Ом, то $R_2 = 32 - 8 = 24$ Ом.</p><p>Оба случая описывают одну и ту же ситуацию: кольцо разделено на два участка с сопротивлениями 8 Ом и 24 Ом.</p><p>Для однородной проволоки сопротивление прямо пропорционально ее длине. Поэтому отношение длин участков будет равно отношению их сопротивлений:</p><p>$\frac{L_1}{L_2} = \frac{R_1}{R_2} = \frac{8}{24} = \frac{1}{3}$</p><p>Следовательно, провода нужно подключить так, чтобы они делили кольцо на части, длины которых относятся как 1 к 3.</p><p><strong>Ответ:</strong> Точки подключения должны делить кольцо в отношении 1:3.</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" => "1319698" "type" => "task" ] "previous" => array:2 [ "refs" => "1319696" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1107 #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" => 1341151 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-190" "field_display_title" => "190" "field_folder" => "1" "field_image_name" => "190" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Book {#1048} ] #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 {#1083 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1117 #items: array:1 [ 0 => App\Models\Element {#1109 #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" => 1519696 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1101} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341151" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "190-1.jpg" "alt" => null "width" => "1620" "height" => 2460 "path" => "/media/fizika_10/gelfgat-z/0-1/190-1.webp?ts=1756642376" ] ] ] #original: array:6 [ "id" => 1519696 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "book_page" => array:2 [ "refs" => "1341151" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "190-1.jpg" "alt" => null "width" => "1620" "height" => 2460 "path" => "/media/fizika_10/gelfgat-z/0-1/190-1.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" => "1341152" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341150" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:2 [ 0 => App\Models\Task {#1228 #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" => 1319697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-1" "field_display_title" => "27.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1230 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:1 [ 0 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:4 [ 0 => App\Models\Branch {#1121} 1 => App\Models\Branch {#1125} 2 => App\Models\Branch {#1129} 3 => App\Models\Branch {#1133} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:2 [ 0 => App\Models\Element {#1102} 1 => App\Models\Element {#1094} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319698" "type" => "task" ] "previous" => array:2 [ "refs" => "1319696" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341151" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-1" "field_display_title" => "27.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229} "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 {#1230} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1232} "content" => Illuminate\Database\Eloquent\Collection {#1233} "next" => array:2 [ "refs" => "1319698" "type" => "task" ] "previous" => array:2 [ "refs" => "1319696" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1234} "page" => array:2 [ "refs" => "1341151" "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 => "*" ] } 1 => App\Models\Task {#1235 #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" => 1319698 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => "191" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-2" "field_display_title" => "27.2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1237 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:1 [ 0 => App\Models\Branch {#1121} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:4 [ 0 => App\Models\Branch {#1121} 1 => App\Models\Branch {#1125} 2 => App\Models\Branch {#1129} 3 => App\Models\Branch {#1133} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:2 [ 0 => App\Models\Element {#1250 #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" => 1493876 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ 0 => App\Models\Edition {#1101} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319698" "type" => "task" ] "text" => "<p><strong>27.2.</strong> Найдите полное сопротивление R показанной на рисунке цепи, если $R_1 = R_2 = R_5 = R_6 = 3,0$ Ом; $R_3 = 20$ Ом, $R_4 = 24$ Ом. Найдите силу тока, идущего через каждый резистор, если к цепи приложено напряжение $U = 36$ В.</p><p>☑ $ R = 18$ Ом; $I_1 = I_6 = 2$ А, $I_3 = 1,2$ А, $I_2 = I_4 = I_5 = 0,8$ А.</p><p><strong><em>Решение.</em></strong> Резисторы 2, 4 и 5 соединены последовательно, $R_{245} = R_2 + R_4 + R_5 = 30$ Ом. Резистор 3 подключен параллельно к этому участку цепи, поэтому</p><p>$R_{2345} = \frac{R_3 R_{245}}{R_3 + R_{245}} = 12 \text{(Ом)}.$</p><p>Резисторы 1 и 6 соединены с участком 2-3-4-5 последовательно, $R = R_1 + R_6 + R_{2345} = 18 \text{(Ом)}$. Через резисторы 1 и 6, включенные в неразветвленную часть цепи, идет весь ток, следовательно: $I_1 = I_6 = I = U/R = 2 \text{(А)}$. На участке же 2-3-4-5 электрический ток разветвляется. Напряжение на этом участке цепи равно $U_3 = I R_{2345} = 24 \text{(В)}$. Согласно закону Ома</p><p>$I_3 = U_3 / R_3 = 1,2 \text{(А)}, I_2 = I_4 = I_5 = U_3 / R_{245} = 0,8 \text{(А)}.$</p><p>Как и следовало ожидать, $I_2 + I_3 = I$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1412" "height" => 1359 "path" => "/media/fizika_10/gelfgat-z/0-27/2-1.webp?ts=1756251100" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1307" "height" => 287 "path" => "/media/fizika_10/gelfgat-z/0-27/2-2.webp?ts=1756251100" ] ] ] #original: array:7 [ "id" => 1493876 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251} "task" => array:2 [ "refs" => "1319698" "type" => "task" ] "text" => "<p><strong>27.2.</strong> Найдите полное сопротивление R показанной на рисунке цепи, если $R_1 = R_2 = R_5 = R_6 = 3,0$ Ом; $R_3 = 20$ Ом, $R_4 = 24$ Ом. Найдите силу тока, идущего через каждый резистор, если к цепи приложено напряжение $U = 36$ В.</p><p>☑ $ R = 18$ Ом; $I_1 = I_6 = 2$ А, $I_3 = 1,2$ А, $I_2 = I_4 = I_5 = 0,8$ А.</p><p><strong><em>Решение.</em></strong> Резисторы 2, 4 и 5 соединены последовательно, $R_{245} = R_2 + R_4 + R_5 = 30$ Ом. Резистор 3 подключен параллельно к этому участку цепи, поэтому</p><p>$R_{2345} = \frac{R_3 R_{245}}{R_3 + R_{245}} = 12 \text{(Ом)}.$</p><p>Резисторы 1 и 6 соединены с участком 2-3-4-5 последовательно, $R = R_1 + R_6 + R_{2345} = 18 \text{(Ом)}$. Через резисторы 1 и 6, включенные в неразветвленную часть цепи, идет весь ток, следовательно: $I_1 = I_6 = I = U/R = 2 \text{(А)}$. На участке же 2-3-4-5 электрический ток разветвляется. Напряжение на этом участке цепи равно $U_3 = I R_{2345} = 24 \text{(В)}$. Согласно закону Ома</p><p>$I_3 = U_3 / R_3 = 1,2 \text{(А)}, I_2 = I_4 = I_5 = U_3 / R_{245} = 0,8 \text{(А)}.$</p><p>Как и следовало ожидать, $I_2 + I_3 = I$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1412" "height" => 1359 "path" => "/media/fizika_10/gelfgat-z/0-27/2-1.webp?ts=1756251100" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1307" "height" => 287 "path" => "/media/fizika_10/gelfgat-z/0-27/2-2.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 {#1252 #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" => 1691433 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ 0 => App\Models\Edition {#1095} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319698" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$R_1 = R_2 = R_5 = R_6 = 3.0$ Ом</p><p>$R_3 = 20$ Ом</p><p>$R_4 = 24$ Ом</p><p>$U = 36$ В</p><p><strong>Найти:</strong></p><p>$R$ - ?; $I_1$ - ?; $I_2$ - ?; $I_3$ - ?; $I_4$ - ?; $I_5$ - ?; $I_6$ - ?</p><p><strong>Решение:</strong></p><p><strong>Найдите полное сопротивление цепи</strong></p><p>Сначала определим эквивалентное сопротивление для разных участков цепи. Резисторы $R_2$, $R_4$ и $R_5$ соединены последовательно. Их общее сопротивление $R_{245}$ равно сумме их сопротивлений:</p><p>$R_{245} = R_2 + R_4 + R_5 = 3.0 + 24 + 3.0 = 30$ Ом.</p><p>Этот участок цепи ($R_{245}$) соединен параллельно с резистором $R_3$. Найдем их общее сопротивление $R_{2345}$:</p><p>$R_{2345} = \frac{R_3 \cdot R_{245}}{R_3 + R_{245}} = \frac{20 \cdot 30}{20 + 30} = \frac{600}{50} = 12$ Ом.</p><p>Резисторы $R_1$ и $R_6$ соединены последовательно с участком $R_{2345}$. Полное сопротивление всей цепи $R$ равно сумме сопротивлений этих трех участков:</p><p>$R = R_1 + R_6 + R_{2345} = 3.0 + 3.0 + 12 = 18$ Ом.</p><p><strong>Ответ:</strong> Полное сопротивление цепи равно 18 Ом.</p><p><strong>Найдите силу тока, идущего через каждый резистор</strong></p><p>Сила тока в неразветвленной части цепи, то есть через резисторы $R_1$ и $R_6$, определяется по закону Ома для всей цепи:</p><p>$I_1 = I_6 = I = \frac{U}{R} = \frac{36 \text{ В}}{18 \text{ Ом}} = 2$ А.</p><p>Далее найдем напряжение на разветвленном участке цепи (участок с сопротивлением $R_{2345}$):</p><p>$U_{2345} = I \cdot R_{2345} = 2 \text{ А} \cdot 12 \text{ Ом} = 24$ В.</p><p>При параллельном соединении напряжение на ветвях одинаково, поэтому напряжение на резисторе $R_3$ равно напряжению на последовательной цепи из резисторов $R_2, R_4, R_5$, и оба равны $U_{2345}$.</p><p>Сила тока через резистор $R_3$:</p><p>$I_3 = \frac{U_{2345}}{R_3} = \frac{24 \text{ В}}{20 \text{ Ом}} = 1.2$ А.</p><p>Сила тока через последовательно соединенные резисторы $R_2, R_4, R_5$:</p><p>$I_2 = I_4 = I_5 = \frac{U_{2345}}{R_{245}} = \frac{24 \text{ В}}{30 \text{ Ом}} = 0.8$ А.</p><p>Проверим правильность расчетов по первому правилу Кирхгофа: ток, входящий в узел, должен быть равен току, выходящему из него. $I = I_3 + I_{245} = 1.2 \text{ А} + 0.8 \text{ А} = 2$ А. Расчеты верны.</p><p><strong>Ответ:</strong> $I_1 = 2$ А; $I_2 = 0.8$ А; $I_3 = 1.2$ А; $I_4 = 0.8$ А; $I_5 = 0.8$ А; $I_6 = 2$ А.</p>" ] #original: array:6 [ "id" => 1691433 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253} "task" => array:2 [ "refs" => "1319698" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$R_1 = R_2 = R_5 = R_6 = 3.0$ Ом</p><p>$R_3 = 20$ Ом</p><p>$R_4 = 24$ Ом</p><p>$U = 36$ В</p><p><strong>Найти:</strong></p><p>$R$ - ?; $I_1$ - ?; $I_2$ - ?; $I_3$ - ?; $I_4$ - ?; $I_5$ - ?; $I_6$ - ?</p><p><strong>Решение:</strong></p><p><strong>Найдите полное сопротивление цепи</strong></p><p>Сначала определим эквивалентное сопротивление для разных участков цепи. Резисторы $R_2$, $R_4$ и $R_5$ соединены последовательно. Их общее сопротивление $R_{245}$ равно сумме их сопротивлений:</p><p>$R_{245} = R_2 + R_4 + R_5 = 3.0 + 24 + 3.0 = 30$ Ом.</p><p>Этот участок цепи ($R_{245}$) соединен параллельно с резистором $R_3$. Найдем их общее сопротивление $R_{2345}$:</p><p>$R_{2345} = \frac{R_3 \cdot R_{245}}{R_3 + R_{245}} = \frac{20 \cdot 30}{20 + 30} = \frac{600}{50} = 12$ Ом.</p><p>Резисторы $R_1$ и $R_6$ соединены последовательно с участком $R_{2345}$. Полное сопротивление всей цепи $R$ равно сумме сопротивлений этих трех участков:</p><p>$R = R_1 + R_6 + R_{2345} = 3.0 + 3.0 + 12 = 18$ Ом.</p><p><strong>Ответ:</strong> Полное сопротивление цепи равно 18 Ом.</p><p><strong>Найдите силу тока, идущего через каждый резистор</strong></p><p>Сила тока в неразветвленной части цепи, то есть через резисторы $R_1$ и $R_6$, определяется по закону Ома для всей цепи:</p><p>$I_1 = I_6 = I = \frac{U}{R} = \frac{36 \text{ В}}{18 \text{ Ом}} = 2$ А.</p><p>Далее найдем напряжение на разветвленном участке цепи (участок с сопротивлением $R_{2345}$):</p><p>$U_{2345} = I \cdot R_{2345} = 2 \text{ А} \cdot 12 \text{ Ом} = 24$ В.</p><p>При параллельном соединении напряжение на ветвях одинаково, поэтому напряжение на резисторе $R_3$ равно напряжению на последовательной цепи из резисторов $R_2, R_4, R_5$, и оба равны $U_{2345}$.</p><p>Сила тока через резистор $R_3$:</p><p>$I_3 = \frac{U_{2345}}{R_3} = \frac{24 \text{ В}}{20 \text{ Ом}} = 1.2$ А.</p><p>Сила тока через последовательно соединенные резисторы $R_2, R_4, R_5$:</p><p>$I_2 = I_4 = I_5 = \frac{U_{2345}}{R_{245}} = \frac{24 \text{ В}}{30 \text{ Ом}} = 0.8$ А.</p><p>Проверим правильность расчетов по первому правилу Кирхгофа: ток, входящий в узел, должен быть равен току, выходящему из него. $I = I_3 + I_{245} = 1.2 \text{ А} + 0.8 \text{ А} = 2$ А. Расчеты верны.</p><p><strong>Ответ:</strong> $I_1 = 2$ А; $I_2 = 0.8$ А; $I_3 = 1.2$ А; $I_4 = 0.8$ А; $I_5 = 0.8$ А; $I_6 = 2$ А.</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" => "1319699" "type" => "task" ] "previous" => array:2 [ "refs" => "1319697" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341151" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319698 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => "191" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-2" "field_display_title" => "27.2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1236} "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 {#1237} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1239} "content" => Illuminate\Database\Eloquent\Collection {#1241} "next" => array:2 [ "refs" => "1319699" "type" => "task" ] "previous" => array:2 [ "refs" => "1319697" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1247} "page" => array:2 [ "refs" => "1341151" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341151 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-190" "field_display_title" => "190" "field_folder" => "1" "field_image_name" => "190" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1088} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1087} "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 {#1083} "content" => Illuminate\Database\Eloquent\Collection {#1117} "next" => array:2 [ "refs" => "1341152" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341150" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1220} ] #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" => 1319697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "190" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/27-1" "field_display_title" => "27.1" "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 {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1111} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1319698" "type" => "task" ] "previous" => array:2 [ "refs" => "1319696" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1105} "page" => array:2 [ "refs" => "1341151" "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 => "*" ] }
№27.1 (с. 190)
Условие. №27.1 (с. 190)
скриншот условия
27.1. Из проволоки сопротивлением $R_0 = 32 \text{ Ом}$ сделано кольцо. В каких точках кольца следует подключить провода, чтобы получить сопротивление $R = 6 \text{ Ом}$?
Точки подключения должны делить кольцо в отношении 1:3.
Решение. Участки кольца соединены между собой параллельно. Обозначим длину кольца $\text{l}$, а длину одного из участков $\text{x}$. Тогда сопротивления участков $R_0x/l$ и $R_0(l-x)/l$, а сопротивление всей цепи $R = R_0x(l-x)/l^2$. Отсюда находим отношение $x/l$: оно равно 0,25 или 0,75. Оба значения соответствуют одному решению — делению кольца на две части в отношении 1:3.
Решение. №27.1 (с. 190)
Дано:
Сопротивление всей проволоки (кольца), $R_0 = 32$ Ом.
Требуемое общее сопротивление, $R = 6$ Ом.
Найти:
Отношение, в котором точки подключения должны делить длину кольца.
Решение:
При подключении проводов к двум точкам на кольце, оно разделяется на два участка (две дуги), которые оказываются соединенными параллельно. Обозначим сопротивления этих участков как $R_1$ и $R_2$.
Так как эти два участка вместе составляют исходную проволоку, сумма их сопротивлений равна общему сопротивлению проволоки:
$R_1 + R_2 = R_0 = 32$ Ом.
Общее сопротивление $R$ при параллельном соединении вычисляется по формуле:
$R = \frac{R_1 R_2}{R_1 + R_2}$
Подставим известные значения $R$ и $R_0$ в эту формулу:
$6 = \frac{R_1 R_2}{32}$
Из этого уравнения можно найти произведение сопротивлений $R_1$ и $R_2$:
$R_1 R_2 = 6 \cdot 32 = 192$ (Ом²)
Таким образом, мы имеем систему из двух уравнений:
1) $R_1 + R_2 = 32$
2) $R_1 R_2 = 192$
Это система уравнений, которую можно решить, например, методом подстановки. Выразим $R_2$ из первого уравнения: $R_2 = 32 - R_1$. Подставим это выражение во второе уравнение:
$R_1 (32 - R_1) = 192$
$32 R_1 - R_1^2 = 192$
Приведем уравнение к стандартному квадратному виду:
$R_1^2 - 32 R_1 + 192 = 0$
Решим это квадратное уравнение. Найдем дискриминант:
$D = b^2 - 4ac = (-32)^2 - 4 \cdot 1 \cdot 192 = 1024 - 768 = 256$
Найдем корни уравнения:
$R_1 = \frac{-b \pm \sqrt{D}}{2a} = \frac{32 \pm \sqrt{256}}{2} = \frac{32 \pm 16}{2}$
Получаем два возможных значения для $R_1$:
$R_{1,1} = \frac{32 + 16}{2} = \frac{48}{2} = 24$ Ом.
$R_{1,2} = \frac{32 - 16}{2} = \frac{16}{2} = 8$ Ом.
Если $R_1 = 24$ Ом, то $R_2 = 32 - 24 = 8$ Ом.
Если $R_1 = 8$ Ом, то $R_2 = 32 - 8 = 24$ Ом.
Оба случая описывают одну и ту же ситуацию: кольцо разделено на два участка с сопротивлениями 8 Ом и 24 Ом.
Для однородной проволоки сопротивление прямо пропорционально ее длине. Поэтому отношение длин участков будет равно отношению их сопротивлений:
$\frac{L_1}{L_2} = \frac{R_1}{R_2} = \frac{8}{24} = \frac{1}{3}$
Следовательно, провода нужно подключить так, чтобы они делили кольцо на части, длины которых относятся как 1 к 3.
Ответ: Точки подключения должны делить кольцо в отношении 1:3.
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 27.1 расположенного на странице 190 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 №27.1 (с. 190), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.