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Номер 33.4, страница 242 - 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. Электромагнитные колебания и волны. 33. Свободные электромагнитные колебания. Переменный ток. Упражнения - номер 33.4, страница 242.
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" => 1319784 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "242" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/33-4" "field_display_title" => "33.4" "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 {#1057 #items: array:1 [ 0 => App\Models\Book {#1056 #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 {#1061 #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: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 {#1063 #items: array:2 [ 0 => App\Models\Term {#1071 #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 {#1072 #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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1068 #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 {#1070 #items: array:3 [ 0 => App\Models\Term {#1077 #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 {#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: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 {#1079 #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 {#1074 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1060 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1073 #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 {#1064 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1088 #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 {#1081 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080 #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 {#1085 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Term {#1084 #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 {#1061} "field_class" => Illuminate\Database\Eloquent\Collection {#1063} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1062} "field_author" => Illuminate\Database\Eloquent\Collection {#1070} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1074} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075} "field_country" => Illuminate\Database\Eloquent\Collection {#1066} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1065} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1081} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080} "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 {#1085} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1092} "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 {#1049 #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 {#1057} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1049} ] #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 {#1115 #items: array:4 [ 0 => 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" => 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 {#1126 #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 {#1127 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 #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 {#1126} "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 {#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 => "*" ] } 1 => 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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "241" "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 {#1132} ] #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 {#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" => 1319372 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Свободные электромагнитные колебания. Переменный ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1135 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Branch {#1143 #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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1146 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_page_start" => "241" "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 {#1146} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147} ] #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" => 1319372 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Свободные электромагнитные колебания. Переменный ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134} "field_page_start" => "241" "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 {#1135} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144} ] #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 {#1137 #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" => 1319373 "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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1140 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1152 #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" => 1319372 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Свободные электромагнитные колебания. Переменный ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1155 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Branch {#1143} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319372 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "33. Свободные электромагнитные колебания. Переменный ток" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1154} "field_page_start" => "241" "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 {#1155} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1156} ] #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" => 1319373 "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 {#1136} "field_page_start" => "241" "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 {#1140} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153} ] #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 {#1106 #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" => 1493935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1105 #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 {#1102 #items: array:1 [ 0 => App\Models\Term {#1104 #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 {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 #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 {#1102} "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 {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "1319784" "type" => "task" ] "text" => "<p><strong>33.4.</strong> Найдите действующее значение $\text{I}$ переменного тока (см. рис. а, б, в).</p><p><em><strong>Решение.</strong></em> Величина $\text{I}$ представляет собой значение силы постоянного тока, при прохождении которого в проводнике выделяется такое же количество теплоты, как и при прохождении данного переменного тока за это же время (т. е. $I^2 = \overline{i^2}$).</p><p><strong>а)</strong> Квадрат силы тока в любой момент равен $I_0^2$. Поэтому $I = I_0$.</p><p><strong>б)</strong> $I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$, откуда $I = I_0/2$.</p><p><strong>в)</strong> $I^2 T = I_0^2 \tau$, откуда $I = I_0 \sqrt{\frac{\tau}{T}}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1408" "height" => 1178 "path" => "/media/fizika_10/gelfgat-z/0-33/4-1.webp?ts=1756251143" ] ] ] #original: array:7 [ "id" => 1493935 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "1319784" "type" => "task" ] "text" => "<p><strong>33.4.</strong> Найдите действующее значение $\text{I}$ переменного тока (см. рис. а, б, в).</p><p><em><strong>Решение.</strong></em> Величина $\text{I}$ представляет собой значение силы постоянного тока, при прохождении которого в проводнике выделяется такое же количество теплоты, как и при прохождении данного переменного тока за это же время (т. е. $I^2 = \overline{i^2}$).</p><p><strong>а)</strong> Квадрат силы тока в любой момент равен $I_0^2$. Поэтому $I = I_0$.</p><p><strong>б)</strong> $I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$, откуда $I = I_0/2$.</p><p><strong>в)</strong> $I^2 T = I_0^2 \tau$, откуда $I = I_0 \sqrt{\frac{\tau}{T}}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1408" "height" => 1178 "path" => "/media/fizika_10/gelfgat-z/0-33/4-1.webp?ts=1756251143" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1098 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1691492 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Edition {#1099 #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 {#1094 #items: array:1 [ 0 => App\Models\Term {#1097 #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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054 #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 {#1094} "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 {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1093} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054} "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" => "1319784" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Графики зависимости мгновенной силы тока $i$ от времени $t$ для трех случаев (рис. а, б, в).</p><p>Амплитудное значение тока: $I_0$.</p><p>Период тока: $T$.</p><p>Длительность импульса для случая в: $\tau$.</p><p><strong>Найти:</strong></p><p>Действующее значение переменного тока $I$ для каждого случая.</p><p><strong>Решение:</strong></p><p>Действующее (или эффективное) значение переменного тока $I$ определяется как значение такого постоянного тока, который за время, равное периоду переменного тока, выделит в проводнике то же количество теплоты, что и данный переменный ток. Квадрат действующего значения $I^2$ равен среднему значению квадрата мгновенной силы тока $i^2$ за период $T$. Это значение вычисляется по формуле:</p><p>$I^2 = \overline{i^2} = \frac{1}{T} \int_0^T i(t)^2 \, dt$</p><p>Соответственно, действующее значение тока равно $I = \sqrt{\overline{i^2}}$.</p><p>Рассчитаем действующее значение тока для каждого из трех представленных случаев.</p><p><strong>а)</strong></p><p>На графике (рис. а) изображен переменный ток прямоугольной формы (меандр). В течение первой половины периода ($0 \le t < T/2$) сила тока равна $I_0$, а в течение второй половины ($T/2 \le t < T$) — $-I_0$.</p><p>Квадрат мгновенного значения силы тока $i^2$ остается постоянным в течение всего периода:</p><p>Если $i = I_0$, то $i^2 = I_0^2$.</p><p>Если $i = -I_0$, то $i^2 = (-I_0)^2 = I_0^2$.</p><p>Таким образом, среднее значение квадрата силы тока за период равно самому этому значению:</p><p>$I^2 = \overline{i^2} = I_0^2$</p><p>Отсюда находим действующее значение тока:</p><p>$I = \sqrt{I_0^2} = I_0$</p><p><strong>Ответ:</strong> $I = I_0$.</p><p><strong>б)</strong></p><p>На графике (рис. б) изображен ток в виде последовательности разнополярных импульсов. Согласно приведенной в задании формуле для решения, будем считать, что за один период $T$ ток принимает значение $I_0$ в течение общего времени $T/8$, значение $-I_0$ в течение общего времени $T/8$, а в остальное время он равен нулю.</p><p>Найдем среднее значение квадрата силы тока за период $T$, используя определение:</p><p>$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt$</p><p>Поскольку ток отличен от нуля только в определенные промежутки времени, интеграл можно разбить на части. Общее количество тепла за период $T$ пропорционально $I^2T$. Это же количество тепла выделяется переменным током:</p><p>$I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$</p><p>Упростим выражение:</p><p>$I^2 T = I_0^2 \frac{T}{8} + I_0^2 \frac{T}{8} = I_0^2 \frac{2T}{8} = I_0^2 \frac{T}{4}$</p><p>Сократив на $T$, получим:</p><p>$I^2 = \frac{I_0^2}{4}$</p><p>Действующее значение тока равно:</p><p>$I = \sqrt{\frac{I_0^2}{4}} = \frac{I_0}{2}$</p><p><strong>Ответ:</strong> $I = I_0/2$.</p><p><strong>в)</strong></p><p>На графике (рис. в) изображен ток в виде последовательности однополярных прямоугольных импульсов. В течение одного периода $T$ ток равен $I_0$ на интервале времени от $0$ до $\tau$ и равен нулю на остальной части периода, от $\tau$ до $T$.</p><p>Найдем среднее значение квадрата силы тока за период $T$:</p><p>$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt = \frac{1}{T} \left( \int_0^\tau (I_0)^2 \, dt + \int_\tau^T (0)^2 \, dt \right)$</p><p>Второй интеграл равен нулю. Вычисляем первый:</p><p>$I^2 = \frac{1}{T} \int_0^\tau I_0^2 \, dt = \frac{I_0^2}{T} [t]_0^\tau = \frac{I_0^2}{T} (\tau - 0) = \frac{I_0^2 \tau}{T}$</p><p>Отсюда находим действующее значение тока:</p><p>$I = \sqrt{\frac{I_0^2 \tau}{T}} = I_0 \sqrt{\frac{\tau}{T}}$</p><p><strong>Ответ:</strong> $I = I_0 \sqrt{\frac{\tau}{T}}$.</p>" ] #original: array:6 [ "id" => 1691492 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052} "task" => array:2 [ "refs" => "1319784" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Графики зависимости мгновенной силы тока $i$ от времени $t$ для трех случаев (рис. а, б, в).</p><p>Амплитудное значение тока: $I_0$.</p><p>Период тока: $T$.</p><p>Длительность импульса для случая в: $\tau$.</p><p><strong>Найти:</strong></p><p>Действующее значение переменного тока $I$ для каждого случая.</p><p><strong>Решение:</strong></p><p>Действующее (или эффективное) значение переменного тока $I$ определяется как значение такого постоянного тока, который за время, равное периоду переменного тока, выделит в проводнике то же количество теплоты, что и данный переменный ток. Квадрат действующего значения $I^2$ равен среднему значению квадрата мгновенной силы тока $i^2$ за период $T$. Это значение вычисляется по формуле:</p><p>$I^2 = \overline{i^2} = \frac{1}{T} \int_0^T i(t)^2 \, dt$</p><p>Соответственно, действующее значение тока равно $I = \sqrt{\overline{i^2}}$.</p><p>Рассчитаем действующее значение тока для каждого из трех представленных случаев.</p><p><strong>а)</strong></p><p>На графике (рис. а) изображен переменный ток прямоугольной формы (меандр). В течение первой половины периода ($0 \le t < T/2$) сила тока равна $I_0$, а в течение второй половины ($T/2 \le t < T$) — $-I_0$.</p><p>Квадрат мгновенного значения силы тока $i^2$ остается постоянным в течение всего периода:</p><p>Если $i = I_0$, то $i^2 = I_0^2$.</p><p>Если $i = -I_0$, то $i^2 = (-I_0)^2 = I_0^2$.</p><p>Таким образом, среднее значение квадрата силы тока за период равно самому этому значению:</p><p>$I^2 = \overline{i^2} = I_0^2$</p><p>Отсюда находим действующее значение тока:</p><p>$I = \sqrt{I_0^2} = I_0$</p><p><strong>Ответ:</strong> $I = I_0$.</p><p><strong>б)</strong></p><p>На графике (рис. б) изображен ток в виде последовательности разнополярных импульсов. Согласно приведенной в задании формуле для решения, будем считать, что за один период $T$ ток принимает значение $I_0$ в течение общего времени $T/8$, значение $-I_0$ в течение общего времени $T/8$, а в остальное время он равен нулю.</p><p>Найдем среднее значение квадрата силы тока за период $T$, используя определение:</p><p>$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt$</p><p>Поскольку ток отличен от нуля только в определенные промежутки времени, интеграл можно разбить на части. Общее количество тепла за период $T$ пропорционально $I^2T$. Это же количество тепла выделяется переменным током:</p><p>$I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$</p><p>Упростим выражение:</p><p>$I^2 T = I_0^2 \frac{T}{8} + I_0^2 \frac{T}{8} = I_0^2 \frac{2T}{8} = I_0^2 \frac{T}{4}$</p><p>Сократив на $T$, получим:</p><p>$I^2 = \frac{I_0^2}{4}$</p><p>Действующее значение тока равно:</p><p>$I = \sqrt{\frac{I_0^2}{4}} = \frac{I_0}{2}$</p><p><strong>Ответ:</strong> $I = I_0/2$.</p><p><strong>в)</strong></p><p>На графике (рис. в) изображен ток в виде последовательности однополярных прямоугольных импульсов. В течение одного периода $T$ ток равен $I_0$ на интервале времени от $0$ до $\tau$ и равен нулю на остальной части периода, от $\tau$ до $T$.</p><p>Найдем среднее значение квадрата силы тока за период $T$:</p><p>$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt = \frac{1}{T} \left( \int_0^\tau (I_0)^2 \, dt + \int_\tau^T (0)^2 \, dt \right)$</p><p>Второй интеграл равен нулю. Вычисляем первый:</p><p>$I^2 = \frac{1}{T} \int_0^\tau I_0^2 \, dt = \frac{I_0^2}{T} [t]_0^\tau = \frac{I_0^2}{T} (\tau - 0) = \frac{I_0^2 \tau}{T}$</p><p>Отсюда находим действующее значение тока:</p><p>$I = \sqrt{\frac{I_0^2 \tau}{T}} = I_0 \sqrt{\frac{\tau}{T}}$</p><p><strong>Ответ:</strong> $I = I_0 \sqrt{\frac{\tau}{T}}$.</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" => "1319785" "type" => "task" ] "previous" => array:2 [ "refs" => "1319783" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1111 #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" => 1341203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "242" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-242" "field_display_title" => "242" "field_folder" => "1" "field_image_name" => "242" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Book {#1056} ] #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 {#1053 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Element {#1113 #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" => 1519748 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Edition {#1105} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341203" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "242-1.jpg" "alt" => null "width" => "1579" "height" => 2445 "path" => "/media/fizika_10/gelfgat-z/0-1/242-1.webp?ts=1756642404" ] ] ] #original: array:6 [ "id" => 1519748 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1120} "book_page" => array:2 [ "refs" => "1341203" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "242-1.jpg" "alt" => null "width" => "1579" "height" => 2445 "path" => "/media/fizika_10/gelfgat-z/0-1/242-1.webp?ts=1756642404" ] ] ] #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" => "1341204" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341202" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:2 [ 0 => App\Models\Task {#1232 #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" => 1319783 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "241" "field_page_end" => "242" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/33-3" "field_display_title" => "33.3" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1233 #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 {#1234 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ 0 => App\Models\Branch {#1125} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:4 [ 0 => App\Models\Branch {#1125} 1 => App\Models\Branch {#1129} 2 => App\Models\Branch {#1133} 3 => App\Models\Branch {#1137} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1238 #items: array:2 [ 0 => App\Models\Element {#1247 #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" => 1493934 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ 0 => App\Models\Edition {#1105} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319783" "type" => "task" ] "text" => "<p><strong>33.3.</strong> На рисунках приведены графики изменений напряжения на конденсаторе колебательного контура и силы тока в катушке этого контура. Найдите емкость конденсатора и индуктивность катушки контура.</p><p>☑ 13000 пФ; 7,6 мкГн.</p><p><strong>Решение.</strong> Из приведенных в условии графиков видно, что период колебаний $T = 2$ мкс, амплитудные значения напряжения и силы тока $U_m = 12$ В, $I_m = 0,5$ А. Согласно закону сохранения энергии $C U_m^2 / 2 = L I_m^2 / 2$. Используя также формулу Томсона $T = 2\pi\sqrt{LC}$, получим окончательно: но: $C = \frac{T \cdot I_m}{2\pi U_m}$, $L = \frac{T \cdot U_m}{2\pi I_m}$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1383" "height" => 197 "path" => "/media/fizika_10/gelfgat-z/0-33/3-1.webp?ts=1756251143" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1398" "height" => 1125 "path" => "/media/fizika_10/gelfgat-z/0-33/3-2.webp?ts=1756251143" ] ] ] #original: array:7 [ "id" => 1493934 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1248} "task" => array:2 [ "refs" => "1319783" "type" => "task" ] "text" => "<p><strong>33.3.</strong> На рисунках приведены графики изменений напряжения на конденсаторе колебательного контура и силы тока в катушке этого контура. Найдите емкость конденсатора и индуктивность катушки контура.</p><p>☑ 13000 пФ; 7,6 мкГн.</p><p><strong>Решение.</strong> Из приведенных в условии графиков видно, что период колебаний $T = 2$ мкс, амплитудные значения напряжения и силы тока $U_m = 12$ В, $I_m = 0,5$ А. Согласно закону сохранения энергии $C U_m^2 / 2 = L I_m^2 / 2$. Используя также формулу Томсона $T = 2\pi\sqrt{LC}$, получим окончательно: но: $C = \frac{T \cdot I_m}{2\pi U_m}$, $L = \frac{T \cdot U_m}{2\pi I_m}$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1383" "height" => 197 "path" => "/media/fizika_10/gelfgat-z/0-33/3-1.webp?ts=1756251143" ] 1 => array:5 [ "name" => "3-2.jpg" "alt" => null "width" => "1398" "height" => 1125 "path" => "/media/fizika_10/gelfgat-z/0-33/3-2.webp?ts=1756251143" ] ] ] #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 {#1249 #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" => 1691491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Edition {#1099} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319783" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>На основе предоставленных графиков определим параметры колебательного контура:</p><p>Амплитудное значение напряжения на конденсаторе: $U_m = 12$ В.</p><p>Амплитудное значение силы тока в катушке: $I_m = 0,5$ А.</p><p>Период колебаний (время одного полного цикла): $T = 2$ мкс.</p><p>Перевод в систему СИ:</p><p>$T = 2 \text{ мкс} = 2 \cdot 10^{-6}$ с.</p><p><strong>Найти:</strong></p><p>Емкость конденсатора $C$ — ?</p><p>Индуктивность катушки $L$ — ?</p><p><strong>Решение:</strong></p><p>В идеальном колебательном контуре (без потерь энергии) полная электромагнитная энергия сохраняется. Энергия периодически переходит из электрического поля конденсатора в магнитное поле катушки и обратно. Максимальная энергия электрического поля конденсатора равна максимальной энергии магнитного поля катушки:</p><p>$W_{C,max} = W_{L,max}$</p><p>Подставим формулы для максимальной энергии:</p><p>$\frac{C U_m^2}{2} = \frac{L I_m^2}{2}$</p><p>Из этого закона сохранения энергии мы получаем первое соотношение между искомыми величинами $C$ и $L$:</p><p>$C U_m^2 = L I_m^2$ (1)</p><p>Вторым уравнением, связывающим параметры контура, является формула Томсона для периода свободных электромагнитных колебаний:</p><p>$T = 2\pi\sqrt{LC}$ (2)</p><p>Таким образом, мы имеем систему из двух уравнений с двумя неизвестными. Решим эту систему.</p><p>Из уравнения (1) выразим индуктивность $L$ через емкость $C$:</p><p>$L = C \frac{U_m^2}{I_m^2}$</p><p>Подставим это выражение для $L$ в формулу Томсона (2):</p><p>$T = 2\pi\sqrt{\left(C \frac{U_m^2}{I_m^2}\right)C} = 2\pi\sqrt{C^2 \frac{U_m^2}{I_m^2}} = 2\pi C \frac{U_m}{I_m}$</p><p>Из полученного соотношения выразим емкость конденсатора $C$:</p><p>$C = \frac{T \cdot I_m}{2\pi U_m}$</p><p>Подставим числовые значения из условия:</p><p>$C = \frac{2 \cdot 10^{-6} \text{ с} \cdot 0,5 \text{ А}}{2\pi \cdot 12 \text{ В}} = \frac{1 \cdot 10^{-6}}{24\pi} \text{ Ф} \approx 0,01326 \cdot 10^{-6} \text{ Ф}$</p><p>Переведем в пикофарады ($1 \text{ пФ} = 10^{-12} \text{ Ф}$):</p><p>$C \approx 13260 \cdot 10^{-12} \text{ Ф} = 13260$ пФ.</p><p>Округляя до двух значащих цифр, получаем $C \approx 13000$ пФ.</p><p>Теперь найдем индуктивность катушки $L$. Из соотношения (1) выразим емкость $C$ через индуктивность $L$:</p><p>$C = L \frac{I_m^2}{U_m^2}$</p><p>Подставим это выражение в формулу Томсона (2):</p><p>$T = 2\pi\sqrt{L \left(L \frac{I_m^2}{U_m^2}\right)} = 2\pi\sqrt{L^2 \frac{I_m^2}{U_m^2}} = 2\pi L \frac{I_m}{U_m}$</p><p>Выразим индуктивность $L$:</p><p>$L = \frac{T \cdot U_m}{2\pi I_m}$</p><p>Подставим числовые значения:</p><p>$L = \frac{2 \cdot 10^{-6} \text{ с} \cdot 12 \text{ В}}{2\pi \cdot 0,5 \text{ А}} = \frac{24 \cdot 10^{-6}}{\pi} \text{ Гн} \approx 7,639 \cdot 10^{-6} \text{ Гн}$</p><p>Переведем в микрогенри ($1 \text{ мкГн} = 10^{-6} \text{ Гн}$):</p><p>$L \approx 7,639$ мкГн.</p><p>Округляя до двух значащих цифр, получаем $L \approx 7,6$ мкГн.</p><p><strong>Ответ:</strong> емкость конденсатора $C \approx 13000$ пФ; индуктивность катушки $L \approx 7,6$ мкГн.</p>" ] #original: array:6 [ "id" => 1691491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1250} "task" => array:2 [ "refs" => "1319783" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>На основе предоставленных графиков определим параметры колебательного контура:</p><p>Амплитудное значение напряжения на конденсаторе: $U_m = 12$ В.</p><p>Амплитудное значение силы тока в катушке: $I_m = 0,5$ А.</p><p>Период колебаний (время одного полного цикла): $T = 2$ мкс.</p><p>Перевод в систему СИ:</p><p>$T = 2 \text{ мкс} = 2 \cdot 10^{-6}$ с.</p><p><strong>Найти:</strong></p><p>Емкость конденсатора $C$ — ?</p><p>Индуктивность катушки $L$ — ?</p><p><strong>Решение:</strong></p><p>В идеальном колебательном контуре (без потерь энергии) полная электромагнитная энергия сохраняется. Энергия периодически переходит из электрического поля конденсатора в магнитное поле катушки и обратно. Максимальная энергия электрического поля конденсатора равна максимальной энергии магнитного поля катушки:</p><p>$W_{C,max} = W_{L,max}$</p><p>Подставим формулы для максимальной энергии:</p><p>$\frac{C U_m^2}{2} = \frac{L I_m^2}{2}$</p><p>Из этого закона сохранения энергии мы получаем первое соотношение между искомыми величинами $C$ и $L$:</p><p>$C U_m^2 = L I_m^2$ (1)</p><p>Вторым уравнением, связывающим параметры контура, является формула Томсона для периода свободных электромагнитных колебаний:</p><p>$T = 2\pi\sqrt{LC}$ (2)</p><p>Таким образом, мы имеем систему из двух уравнений с двумя неизвестными. Решим эту систему.</p><p>Из уравнения (1) выразим индуктивность $L$ через емкость $C$:</p><p>$L = C \frac{U_m^2}{I_m^2}$</p><p>Подставим это выражение для $L$ в формулу Томсона (2):</p><p>$T = 2\pi\sqrt{\left(C \frac{U_m^2}{I_m^2}\right)C} = 2\pi\sqrt{C^2 \frac{U_m^2}{I_m^2}} = 2\pi C \frac{U_m}{I_m}$</p><p>Из полученного соотношения выразим емкость конденсатора $C$:</p><p>$C = \frac{T \cdot I_m}{2\pi U_m}$</p><p>Подставим числовые значения из условия:</p><p>$C = \frac{2 \cdot 10^{-6} \text{ с} \cdot 0,5 \text{ А}}{2\pi \cdot 12 \text{ В}} = \frac{1 \cdot 10^{-6}}{24\pi} \text{ Ф} \approx 0,01326 \cdot 10^{-6} \text{ Ф}$</p><p>Переведем в пикофарады ($1 \text{ пФ} = 10^{-12} \text{ Ф}$):</p><p>$C \approx 13260 \cdot 10^{-12} \text{ Ф} = 13260$ пФ.</p><p>Округляя до двух значащих цифр, получаем $C \approx 13000$ пФ.</p><p>Теперь найдем индуктивность катушки $L$. Из соотношения (1) выразим емкость $C$ через индуктивность $L$:</p><p>$C = L \frac{I_m^2}{U_m^2}$</p><p>Подставим это выражение в формулу Томсона (2):</p><p>$T = 2\pi\sqrt{L \left(L \frac{I_m^2}{U_m^2}\right)} = 2\pi\sqrt{L^2 \frac{I_m^2}{U_m^2}} = 2\pi L \frac{I_m}{U_m}$</p><p>Выразим индуктивность $L$:</p><p>$L = \frac{T \cdot U_m}{2\pi I_m}$</p><p>Подставим числовые значения:</p><p>$L = \frac{2 \cdot 10^{-6} \text{ с} \cdot 12 \text{ В}}{2\pi \cdot 0,5 \text{ А}} = \frac{24 \cdot 10^{-6}}{\pi} \text{ Гн} \approx 7,639 \cdot 10^{-6} \text{ Гн}$</p><p>Переведем в микрогенри ($1 \text{ мкГн} = 10^{-6} \text{ Гн}$):</p><p>$L \approx 7,639$ мкГн.</p><p>Округляя до двух значащих цифр, получаем $L \approx 7,6$ мкГн.</p><p><strong>Ответ:</strong> емкость конденсатора $C \approx 13000$ пФ; индуктивность катушки $L \approx 7,6$ мкГн.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] 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№33.4 (с. 242)
Условие. №33.4 (с. 242)
скриншот условия
33.4. Найдите действующее значение $\text{I}$ переменного тока (см. рис. а, б, в).
Решение. Величина $\text{I}$ представляет собой значение силы постоянного тока, при прохождении которого в проводнике выделяется такое же количество теплоты, как и при прохождении данного переменного тока за это же время (т. е. $I^2 = \overline{i^2}$).
а) Квадрат силы тока в любой момент равен $I_0^2$. Поэтому $I = I_0$.
б) $I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$, откуда $I = I_0/2$.
в) $I^2 T = I_0^2 \tau$, откуда $I = I_0 \sqrt{\frac{\tau}{T}}$.
Решение. №33.4 (с. 242)
Дано:
Графики зависимости мгновенной силы тока $i$ от времени $t$ для трех случаев (рис. а, б, в).
Амплитудное значение тока: $I_0$.
Период тока: $T$.
Длительность импульса для случая в: $\tau$.
Найти:
Действующее значение переменного тока $I$ для каждого случая.
Решение:
Действующее (или эффективное) значение переменного тока $I$ определяется как значение такого постоянного тока, который за время, равное периоду переменного тока, выделит в проводнике то же количество теплоты, что и данный переменный ток. Квадрат действующего значения $I^2$ равен среднему значению квадрата мгновенной силы тока $i^2$ за период $T$. Это значение вычисляется по формуле:
$I^2 = \overline{i^2} = \frac{1}{T} \int_0^T i(t)^2 \, dt$
Соответственно, действующее значение тока равно $I = \sqrt{\overline{i^2}}$.
Рассчитаем действующее значение тока для каждого из трех представленных случаев.
а)
На графике (рис. а) изображен переменный ток прямоугольной формы (меандр). В течение первой половины периода ($0 \le t < T/2$) сила тока равна $I_0$, а в течение второй половины ($T/2 \le t < T$) — $-I_0$.
Квадрат мгновенного значения силы тока $i^2$ остается постоянным в течение всего периода:
Если $i = I_0$, то $i^2 = I_0^2$.
Если $i = -I_0$, то $i^2 = (-I_0)^2 = I_0^2$.
Таким образом, среднее значение квадрата силы тока за период равно самому этому значению:
$I^2 = \overline{i^2} = I_0^2$
Отсюда находим действующее значение тока:
$I = \sqrt{I_0^2} = I_0$
Ответ: $I = I_0$.
б)
На графике (рис. б) изображен ток в виде последовательности разнополярных импульсов. Согласно приведенной в задании формуле для решения, будем считать, что за один период $T$ ток принимает значение $I_0$ в течение общего времени $T/8$, значение $-I_0$ в течение общего времени $T/8$, а в остальное время он равен нулю.
Найдем среднее значение квадрата силы тока за период $T$, используя определение:
$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt$
Поскольку ток отличен от нуля только в определенные промежутки времени, интеграл можно разбить на части. Общее количество тепла за период $T$ пропорционально $I^2T$. Это же количество тепла выделяется переменным током:
$I^2 T = I_0^2 \cdot \frac{T}{8} + (-I_0)^2 \cdot \frac{T}{8}$
Упростим выражение:
$I^2 T = I_0^2 \frac{T}{8} + I_0^2 \frac{T}{8} = I_0^2 \frac{2T}{8} = I_0^2 \frac{T}{4}$
Сократив на $T$, получим:
$I^2 = \frac{I_0^2}{4}$
Действующее значение тока равно:
$I = \sqrt{\frac{I_0^2}{4}} = \frac{I_0}{2}$
Ответ: $I = I_0/2$.
в)
На графике (рис. в) изображен ток в виде последовательности однополярных прямоугольных импульсов. В течение одного периода $T$ ток равен $I_0$ на интервале времени от $0$ до $\tau$ и равен нулю на остальной части периода, от $\tau$ до $T$.
Найдем среднее значение квадрата силы тока за период $T$:
$I^2 = \frac{1}{T} \int_0^T i(t)^2 \, dt = \frac{1}{T} \left( \int_0^\tau (I_0)^2 \, dt + \int_\tau^T (0)^2 \, dt \right)$
Второй интеграл равен нулю. Вычисляем первый:
$I^2 = \frac{1}{T} \int_0^\tau I_0^2 \, dt = \frac{I_0^2}{T} [t]_0^\tau = \frac{I_0^2}{T} (\tau - 0) = \frac{I_0^2 \tau}{T}$
Отсюда находим действующее значение тока:
$I = \sqrt{\frac{I_0^2 \tau}{T}} = I_0 \sqrt{\frac{\tau}{T}}$
Ответ: $I = I_0 \sqrt{\frac{\tau}{T}}$.
Другие задания:
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