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Номер 5, страница 12, часть 3 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 3
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 3. Глава 7. Электромагнитные колебания и волны. Параграф 37. Колебательный контур. Свободные электромагнитные колебания - номер 5, страница 12.
App\Models\Task {#1024 // 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" => 1435191 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "12" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/37-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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_page_start" => "3" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 1203 "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 {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #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 {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 #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" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #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 {#1040 #items: array:4 [ 0 => App\Models\Term {#1041 #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" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "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 {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "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 => "*" ] } 2 => App\Models\Term {#1043 #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" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "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 => "*" ] } 3 => App\Models\Term {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "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 {#1045 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #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 {#1048 #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: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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1052 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "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_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "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_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => 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_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => 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" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "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" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "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" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "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 {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1045} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046} "field_country" => Illuminate\Database\Eloquent\Collection {#1048} "field_city" => Illuminate\Database\Eloquent\Collection {#1050} "field_series" => Illuminate\Database\Eloquent\Collection {#1052} "field_umk" => Illuminate\Database\Eloquent\Collection {#1053} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1060} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #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 {#1065 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "3" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065} ] #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 {#1066 #items: array:3 [ 0 => App\Models\Branch {#1067 #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" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1033} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1069 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1068} "field_page_start" => "3" "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 {#1069} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1071 #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" => 1434848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 #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:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "3" "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 {#1074 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Branch {#1023} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "3" "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 {#1074} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075} ] #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 {#1076 #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" => 1434850 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Колебательный контур. Свободные электромагнитные колебания" "field_branch_order" => "37" "field_url" => null "field_branch_type" => 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:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "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_page_start" => "9" "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 {#1079 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Branch {#1081 #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" => 1434848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1083 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434848 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "7" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1082} "field_page_start" => "3" "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 {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1084} ] #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" => 1434850 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Колебательный контур. Свободные электромагнитные колебания" "field_branch_order" => "37" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_page_start" => "9" "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 {#1079} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1080} ] #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 {#1122 #items: array:2 [ 0 => App\Models\Element {#1123 #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" => 1698579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Edition {#1125 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1128 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1126} "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 {#1128} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1129} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1130} "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" => "1435191" "type" => "task" ] "text" => "<p><strong>5.</strong> На рис. 14 показан график зависимости от времени $\text{t}$ напряжения $\text{u}$ между обкладками конденсатора колебательного контура при свободных колебаниях в нём для промежутка времени $0 < t < 6$ мкс. Ёмкость конденсатора равна $C = 10$ нФ.</p><p>Рис. 14</p><p>Используя данную зависимость, определите</p><p><strong>а) напряжение между обкладками конденсатора в моменты времени</strong> $t_1 = 0$, $t_2 = 0,5$ мкс, $t_3 = 0,75$ мкс, $t_4 = 1$ мкс, $t_5 = 1,5$ мкс, $t_6 = 1,75$ мкс, $t_7 = 2$ мкс</p><p>$U_1 = \text{\_\_\_\_\_\_}$, $U_2 = \text{\_\_\_\_\_\_}$, $U_3 = \text{\_\_\_\_\_\_}$, $U_4 = \text{\_\_\_\_\_\_}$, $U_5 = \text{\_\_\_\_\_\_}$</p><p>$U_6 = \text{\_\_\_\_\_\_}$, $U_7 = \text{\_\_\_\_\_\_}$</p><p><strong>б) изменение суммы электрической и магнитной энергии контура за промежутки времени</strong> $\Delta t_1 = t_2 - t_1$, $\Delta t_2 = t_4 - t_2$, $\Delta t_3 = t_5 - t_4$, $\Delta t_4 = t_7 - t_5$</p><p>$\Delta W_1 = \text{\_\_\_\_\_\_}$, $\Delta W_2 = \text{\_\_\_\_\_\_}$</p><p>$\Delta W_3 = \text{\_\_\_\_\_\_}$, $\Delta W_4 = \text{\_\_\_\_\_\_}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "2017" "height" => 1932 "path" => "/media/fizika_09/grachev-rt/0-37/5-1.webp?ts=1759402812" ] ] ] #original: array:7 [ "id" => 1698579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1124} "task" => array:2 [ "refs" => "1435191" "type" => "task" ] "text" => "<p><strong>5.</strong> На рис. 14 показан график зависимости от времени $\text{t}$ напряжения $\text{u}$ между обкладками конденсатора колебательного контура при свободных колебаниях в нём для промежутка времени $0 < t < 6$ мкс. Ёмкость конденсатора равна $C = 10$ нФ.</p><p>Рис. 14</p><p>Используя данную зависимость, определите</p><p><strong>а) напряжение между обкладками конденсатора в моменты времени</strong> $t_1 = 0$, $t_2 = 0,5$ мкс, $t_3 = 0,75$ мкс, $t_4 = 1$ мкс, $t_5 = 1,5$ мкс, $t_6 = 1,75$ мкс, $t_7 = 2$ мкс</p><p>$U_1 = \text{\_\_\_\_\_\_}$, $U_2 = \text{\_\_\_\_\_\_}$, $U_3 = \text{\_\_\_\_\_\_}$, $U_4 = \text{\_\_\_\_\_\_}$, $U_5 = \text{\_\_\_\_\_\_}$</p><p>$U_6 = \text{\_\_\_\_\_\_}$, $U_7 = \text{\_\_\_\_\_\_}$</p><p><strong>б) изменение суммы электрической и магнитной энергии контура за промежутки времени</strong> $\Delta t_1 = t_2 - t_1$, $\Delta t_2 = t_4 - t_2$, $\Delta t_3 = t_5 - t_4$, $\Delta t_4 = t_7 - t_5$</p><p>$\Delta W_1 = \text{\_\_\_\_\_\_}$, $\Delta W_2 = \text{\_\_\_\_\_\_}$</p><p>$\Delta W_3 = \text{\_\_\_\_\_\_}$, $\Delta W_4 = \text{\_\_\_\_\_\_}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "2017" "height" => 1932 "path" => "/media/fizika_09/grachev-rt/0-37/5-1.webp?ts=1759402812" ] ] ] #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 {#1131 #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" => 1734565 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Edition {#1133 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1136 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134} "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 {#1136} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1137} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1138} "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" => "1435191" "type" => "task" ] "text" => "<p><strong>а)</strong> Напряжение между обкладками конденсатора в указанные моменты времени определяется непосредственно из графика. Цена деления по оси времени $t$ составляет 0,25 мкс, а по оси напряжения $u$ — 1 В.</p><p>При $t_1 = 0$ мкс напряжение достигает максимального значения: $U_1 = 15$ В.<br>При $t_2 = 0,5$ мкс напряжение достигает минимального значения (первый минимум): $U_2 = -12$ В.<br>При $t_3 = 0,75$ мкс график пересекает ось времени: $U_3 = 0$ В.<br>При $t_4 = 1$ мкс напряжение достигает второго максимума: $U_4 = 10$ В.<br>При $t_5 = 1,5$ мкс напряжение достигает второго минимума: $U_5 = -8$ В.<br>При $t_6 = 1,75$ мкс график пересекает ось времени: $U_6 = 0$ В.<br>При $t_7 = 2$ мкс напряжение достигает третьего максимума: $U_7 = 7$ В.</p><p><strong>Ответ:</strong> $U_1 = 15 \text{ В}, U_2 = -12 \text{ В}, U_3 = 0 \text{ В}, U_4 = 10 \text{ В}, U_5 = -8 \text{ В}, U_6 = 0 \text{ В}, U_7 = 7 \text{ В}$.</p><p><strong>б)</strong> Изменение суммы электрической и магнитной энергии контура — это изменение полной энергии колебательного контура $\Delta W$.</p><p><strong>Дано:</strong></p><p>$C = 10 \text{ нФ}$<br>Из графика (пункт а):<br>$t_1 = 0 \text{ мкс}, U_1 = 15 \text{ В}$<br>$t_2 = 0,5 \text{ мкс}, U_2 = -12 \text{ В}$<br>$t_4 = 1 \text{ мкс}, U_4 = 10 \text{ В}$<br>$t_5 = 1,5 \text{ мкс}, U_5 = -8 \text{ В}$<br>$t_7 = 2 \text{ мкс}, U_7 = 7 \text{ В}$<br></p><p>$C = 10 \text{ нФ} = 10 \cdot 10^{-9} \text{ Ф} = 10^{-8} \text{ Ф}$</p><p><strong>Найти:</strong></p><p>$\Delta W_1, \Delta W_2, \Delta W_3, \Delta W_4$</p><p><strong>Решение:</strong></p><p>Полная энергия колебательного контура в любой момент времени $t$ складывается из энергии электрического поля конденсатора $W_э$ и энергии магнитного поля катушки $W_м$:</p><p>$W(t) = W_э + W_м = \frac{C u^2(t)}{2} + \frac{L i^2(t)}{2}$</p><p>В моменты времени, когда напряжение на конденсаторе достигает своего максимального или минимального значения (амплитудные значения), ток в катушке равен нулю ($i=0$). В эти моменты вся энергия контура сосредоточена в конденсаторе и является чисто электрической:</p><p>$W(t) = \frac{C u^2(t)}{2}$</p><p>Все моменты времени, для которых нужно найти изменение энергии ($\Delta t_1 = t_2 - t_1, \Delta t_2 = t_4 - t_2, \Delta t_3 = t_5 - t_4, \Delta t_4 = t_7 - t_5$), соответствуют экстремумам напряжения. Поэтому мы можем рассчитать полную энергию в начальный и конечный моменты каждого промежутка.</p><p>Вычислим полную энергию контура в каждый из этих моментов:</p><p>$W_1 = W(t_1) = \frac{C U_1^2}{2} = \frac{10^{-8} \cdot 15^2}{2} = \frac{10^{-8} \cdot 225}{2} = 112,5 \cdot 10^{-8} \text{ Дж} = 1,125 \text{ мкДж}$</p><p>$W_2 = W(t_2) = \frac{C U_2^2}{2} = \frac{10^{-8} \cdot (-12)^2}{2} = \frac{10^{-8} \cdot 144}{2} = 72 \cdot 10^{-8} \text{ Дж} = 0,72 \text{ мкДж}$</p><p>$W_4 = W(t_4) = \frac{C U_4^2}{2} = \frac{10^{-8} \cdot 10^2}{2} = \frac{10^{-8} \cdot 100}{2} = 50 \cdot 10^{-8} \text{ Дж} = 0,5 \text{ мкДж}$</p><p>$W_5 = W(t_5) = \frac{C U_5^2}{2} = \frac{10^{-8} \cdot (-8)^2}{2} = \frac{10^{-8} \cdot 64}{2} = 32 \cdot 10^{-8} \text{ Дж} = 0,32 \text{ мкДж}$</p><p>$W_7 = W(t_7) = \frac{C U_7^2}{2} = \frac{10^{-8} \cdot 7^2}{2} = \frac{10^{-8} \cdot 49}{2} = 24,5 \cdot 10^{-8} \text{ Дж} = 0,245 \text{ мкДж}$</p><p>Теперь найдем изменения энергии за указанные промежутки времени:</p><p>$\Delta W_1 = W_2 - W_1 = 0,72 \text{ мкДж} - 1,125 \text{ мкДж} = -0,405 \text{ мкДж}$</p><p>$\Delta W_2 = W_4 - W_2 = 0,5 \text{ мкДж} - 0,72 \text{ мкДж} = -0,22 \text{ мкДж}$</p><p>$\Delta W_3 = W_5 - W_4 = 0,32 \text{ мкДж} - 0,5 \text{ мкДж} = -0,18 \text{ мкДж}$</p><p>$\Delta W_4 = W_7 - W_5 = 0,245 \text{ мкДж} - 0,32 \text{ мкДж} = -0,075 \text{ мкДж}$</p><p>Отрицательное значение изменения энергии означает, что энергия в контуре затухает (уменьшается) со временем.</p><p><strong>Ответ:</strong> $\Delta W_1 = -0,405 \text{ мкДж}, \Delta W_2 = -0,22 \text{ мкДж}, \Delta W_3 = -0,18 \text{ мкДж}, \Delta W_4 = -0,075 \text{ мкДж}$.</p>" ] #original: array:6 [ "id" => 1734565 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1132} "task" => array:2 [ "refs" => "1435191" "type" => "task" ] "text" => "<p><strong>а)</strong> Напряжение между обкладками конденсатора в указанные моменты времени определяется непосредственно из графика. Цена деления по оси времени $t$ составляет 0,25 мкс, а по оси напряжения $u$ — 1 В.</p><p>При $t_1 = 0$ мкс напряжение достигает максимального значения: $U_1 = 15$ В.<br>При $t_2 = 0,5$ мкс напряжение достигает минимального значения (первый минимум): $U_2 = -12$ В.<br>При $t_3 = 0,75$ мкс график пересекает ось времени: $U_3 = 0$ В.<br>При $t_4 = 1$ мкс напряжение достигает второго максимума: $U_4 = 10$ В.<br>При $t_5 = 1,5$ мкс напряжение достигает второго минимума: $U_5 = -8$ В.<br>При $t_6 = 1,75$ мкс график пересекает ось времени: $U_6 = 0$ В.<br>При $t_7 = 2$ мкс напряжение достигает третьего максимума: $U_7 = 7$ В.</p><p><strong>Ответ:</strong> $U_1 = 15 \text{ В}, U_2 = -12 \text{ В}, U_3 = 0 \text{ В}, U_4 = 10 \text{ В}, U_5 = -8 \text{ В}, U_6 = 0 \text{ В}, U_7 = 7 \text{ В}$.</p><p><strong>б)</strong> Изменение суммы электрической и магнитной энергии контура — это изменение полной энергии колебательного контура $\Delta W$.</p><p><strong>Дано:</strong></p><p>$C = 10 \text{ нФ}$<br>Из графика (пункт а):<br>$t_1 = 0 \text{ мкс}, U_1 = 15 \text{ В}$<br>$t_2 = 0,5 \text{ мкс}, U_2 = -12 \text{ В}$<br>$t_4 = 1 \text{ мкс}, U_4 = 10 \text{ В}$<br>$t_5 = 1,5 \text{ мкс}, U_5 = -8 \text{ В}$<br>$t_7 = 2 \text{ мкс}, U_7 = 7 \text{ В}$<br></p><p>$C = 10 \text{ нФ} = 10 \cdot 10^{-9} \text{ Ф} = 10^{-8} \text{ Ф}$</p><p><strong>Найти:</strong></p><p>$\Delta W_1, \Delta W_2, \Delta W_3, \Delta W_4$</p><p><strong>Решение:</strong></p><p>Полная энергия колебательного контура в любой момент времени $t$ складывается из энергии электрического поля конденсатора $W_э$ и энергии магнитного поля катушки $W_м$:</p><p>$W(t) = W_э + W_м = \frac{C u^2(t)}{2} + \frac{L i^2(t)}{2}$</p><p>В моменты времени, когда напряжение на конденсаторе достигает своего максимального или минимального значения (амплитудные значения), ток в катушке равен нулю ($i=0$). В эти моменты вся энергия контура сосредоточена в конденсаторе и является чисто электрической:</p><p>$W(t) = \frac{C u^2(t)}{2}$</p><p>Все моменты времени, для которых нужно найти изменение энергии ($\Delta t_1 = t_2 - t_1, \Delta t_2 = t_4 - t_2, \Delta t_3 = t_5 - t_4, \Delta t_4 = t_7 - t_5$), соответствуют экстремумам напряжения. Поэтому мы можем рассчитать полную энергию в начальный и конечный моменты каждого промежутка.</p><p>Вычислим полную энергию контура в каждый из этих моментов:</p><p>$W_1 = W(t_1) = \frac{C U_1^2}{2} = \frac{10^{-8} \cdot 15^2}{2} = \frac{10^{-8} \cdot 225}{2} = 112,5 \cdot 10^{-8} \text{ Дж} = 1,125 \text{ мкДж}$</p><p>$W_2 = W(t_2) = \frac{C U_2^2}{2} = \frac{10^{-8} \cdot (-12)^2}{2} = \frac{10^{-8} \cdot 144}{2} = 72 \cdot 10^{-8} \text{ Дж} = 0,72 \text{ мкДж}$</p><p>$W_4 = W(t_4) = \frac{C U_4^2}{2} = \frac{10^{-8} \cdot 10^2}{2} = \frac{10^{-8} \cdot 100}{2} = 50 \cdot 10^{-8} \text{ Дж} = 0,5 \text{ мкДж}$</p><p>$W_5 = W(t_5) = \frac{C U_5^2}{2} = \frac{10^{-8} \cdot (-8)^2}{2} = \frac{10^{-8} \cdot 64}{2} = 32 \cdot 10^{-8} \text{ Дж} = 0,32 \text{ мкДж}$</p><p>$W_7 = W(t_7) = \frac{C U_7^2}{2} = \frac{10^{-8} \cdot 7^2}{2} = \frac{10^{-8} \cdot 49}{2} = 24,5 \cdot 10^{-8} \text{ Дж} = 0,245 \text{ мкДж}$</p><p>Теперь найдем изменения энергии за указанные промежутки времени:</p><p>$\Delta W_1 = W_2 - W_1 = 0,72 \text{ мкДж} - 1,125 \text{ мкДж} = -0,405 \text{ мкДж}$</p><p>$\Delta W_2 = W_4 - W_2 = 0,5 \text{ мкДж} - 0,72 \text{ мкДж} = -0,22 \text{ мкДж}$</p><p>$\Delta W_3 = W_5 - W_4 = 0,32 \text{ мкДж} - 0,5 \text{ мкДж} = -0,18 \text{ мкДж}$</p><p>$\Delta W_4 = W_7 - W_5 = 0,245 \text{ мкДж} - 0,32 \text{ мкДж} = -0,075 \text{ мкДж}$</p><p>Отрицательное значение изменения энергии означает, что энергия в контуре затухает (уменьшается) со временем.</p><p><strong>Ответ:</strong> $\Delta W_1 = -0,405 \text{ мкДж}, \Delta W_2 = -0,22 \text{ мкДж}, \Delta W_3 = -0,18 \text{ мкДж}, \Delta W_4 = -0,075 \text{ мкДж}$.</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 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"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" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "3" "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 {#1201 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1199 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1168} "field_page_start" => "3" "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 {#1201} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1199} ] #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_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Book {#1167 #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" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => 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№5 (с. 12)
Условие. №5 (с. 12)
скриншот условия
5. На рис. 14 показан график зависимости от времени $\text{t}$ напряжения $\text{u}$ между обкладками конденсатора колебательного контура при свободных колебаниях в нём для промежутка времени $0 < t < 6$ мкс. Ёмкость конденсатора равна $C = 10$ нФ.
Рис. 14
Используя данную зависимость, определите
а) напряжение между обкладками конденсатора в моменты времени $t_1 = 0$, $t_2 = 0,5$ мкс, $t_3 = 0,75$ мкс, $t_4 = 1$ мкс, $t_5 = 1,5$ мкс, $t_6 = 1,75$ мкс, $t_7 = 2$ мкс
$U_1 = \text{\_\_\_\_\_\_}$, $U_2 = \text{\_\_\_\_\_\_}$, $U_3 = \text{\_\_\_\_\_\_}$, $U_4 = \text{\_\_\_\_\_\_}$, $U_5 = \text{\_\_\_\_\_\_}$
$U_6 = \text{\_\_\_\_\_\_}$, $U_7 = \text{\_\_\_\_\_\_}$
б) изменение суммы электрической и магнитной энергии контура за промежутки времени $\Delta t_1 = t_2 - t_1$, $\Delta t_2 = t_4 - t_2$, $\Delta t_3 = t_5 - t_4$, $\Delta t_4 = t_7 - t_5$
$\Delta W_1 = \text{\_\_\_\_\_\_}$, $\Delta W_2 = \text{\_\_\_\_\_\_}$
$\Delta W_3 = \text{\_\_\_\_\_\_}$, $\Delta W_4 = \text{\_\_\_\_\_\_}$
Решение. №5 (с. 12)
а) Напряжение между обкладками конденсатора в указанные моменты времени определяется непосредственно из графика. Цена деления по оси времени $t$ составляет 0,25 мкс, а по оси напряжения $u$ — 1 В.
При $t_1 = 0$ мкс напряжение достигает максимального значения: $U_1 = 15$ В.
При $t_2 = 0,5$ мкс напряжение достигает минимального значения (первый минимум): $U_2 = -12$ В.
При $t_3 = 0,75$ мкс график пересекает ось времени: $U_3 = 0$ В.
При $t_4 = 1$ мкс напряжение достигает второго максимума: $U_4 = 10$ В.
При $t_5 = 1,5$ мкс напряжение достигает второго минимума: $U_5 = -8$ В.
При $t_6 = 1,75$ мкс график пересекает ось времени: $U_6 = 0$ В.
При $t_7 = 2$ мкс напряжение достигает третьего максимума: $U_7 = 7$ В.
Ответ: $U_1 = 15 \text{ В}, U_2 = -12 \text{ В}, U_3 = 0 \text{ В}, U_4 = 10 \text{ В}, U_5 = -8 \text{ В}, U_6 = 0 \text{ В}, U_7 = 7 \text{ В}$.
б) Изменение суммы электрической и магнитной энергии контура — это изменение полной энергии колебательного контура $\Delta W$.
Дано:
$C = 10 \text{ нФ}$
Из графика (пункт а):
$t_1 = 0 \text{ мкс}, U_1 = 15 \text{ В}$
$t_2 = 0,5 \text{ мкс}, U_2 = -12 \text{ В}$
$t_4 = 1 \text{ мкс}, U_4 = 10 \text{ В}$
$t_5 = 1,5 \text{ мкс}, U_5 = -8 \text{ В}$
$t_7 = 2 \text{ мкс}, U_7 = 7 \text{ В}$
$C = 10 \text{ нФ} = 10 \cdot 10^{-9} \text{ Ф} = 10^{-8} \text{ Ф}$
Найти:
$\Delta W_1, \Delta W_2, \Delta W_3, \Delta W_4$
Решение:
Полная энергия колебательного контура в любой момент времени $t$ складывается из энергии электрического поля конденсатора $W_э$ и энергии магнитного поля катушки $W_м$:
$W(t) = W_э + W_м = \frac{C u^2(t)}{2} + \frac{L i^2(t)}{2}$
В моменты времени, когда напряжение на конденсаторе достигает своего максимального или минимального значения (амплитудные значения), ток в катушке равен нулю ($i=0$). В эти моменты вся энергия контура сосредоточена в конденсаторе и является чисто электрической:
$W(t) = \frac{C u^2(t)}{2}$
Все моменты времени, для которых нужно найти изменение энергии ($\Delta t_1 = t_2 - t_1, \Delta t_2 = t_4 - t_2, \Delta t_3 = t_5 - t_4, \Delta t_4 = t_7 - t_5$), соответствуют экстремумам напряжения. Поэтому мы можем рассчитать полную энергию в начальный и конечный моменты каждого промежутка.
Вычислим полную энергию контура в каждый из этих моментов:
$W_1 = W(t_1) = \frac{C U_1^2}{2} = \frac{10^{-8} \cdot 15^2}{2} = \frac{10^{-8} \cdot 225}{2} = 112,5 \cdot 10^{-8} \text{ Дж} = 1,125 \text{ мкДж}$
$W_2 = W(t_2) = \frac{C U_2^2}{2} = \frac{10^{-8} \cdot (-12)^2}{2} = \frac{10^{-8} \cdot 144}{2} = 72 \cdot 10^{-8} \text{ Дж} = 0,72 \text{ мкДж}$
$W_4 = W(t_4) = \frac{C U_4^2}{2} = \frac{10^{-8} \cdot 10^2}{2} = \frac{10^{-8} \cdot 100}{2} = 50 \cdot 10^{-8} \text{ Дж} = 0,5 \text{ мкДж}$
$W_5 = W(t_5) = \frac{C U_5^2}{2} = \frac{10^{-8} \cdot (-8)^2}{2} = \frac{10^{-8} \cdot 64}{2} = 32 \cdot 10^{-8} \text{ Дж} = 0,32 \text{ мкДж}$
$W_7 = W(t_7) = \frac{C U_7^2}{2} = \frac{10^{-8} \cdot 7^2}{2} = \frac{10^{-8} \cdot 49}{2} = 24,5 \cdot 10^{-8} \text{ Дж} = 0,245 \text{ мкДж}$
Теперь найдем изменения энергии за указанные промежутки времени:
$\Delta W_1 = W_2 - W_1 = 0,72 \text{ мкДж} - 1,125 \text{ мкДж} = -0,405 \text{ мкДж}$
$\Delta W_2 = W_4 - W_2 = 0,5 \text{ мкДж} - 0,72 \text{ мкДж} = -0,22 \text{ мкДж}$
$\Delta W_3 = W_5 - W_4 = 0,32 \text{ мкДж} - 0,5 \text{ мкДж} = -0,18 \text{ мкДж}$
$\Delta W_4 = W_7 - W_5 = 0,245 \text{ мкДж} - 0,32 \text{ мкДж} = -0,075 \text{ мкДж}$
Отрицательное значение изменения энергии означает, что энергия в контуре затухает (уменьшается) со временем.
Ответ: $\Delta W_1 = -0,405 \text{ мкДж}, \Delta W_2 = -0,22 \text{ мкДж}, \Delta W_3 = -0,18 \text{ мкДж}, \Delta W_4 = -0,075 \text{ мкДж}$.
Другие задания:
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