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Номер 107, страница 186 - 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. Электрическое поле. 25. Электрическая емкость. Конденсатор. Энергия электрического поля. Олимпиадные задачи - номер 107, страница 186.
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" => 1319693 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "186" "field_page_end" => "187" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-107" "field_display_title" => "107" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#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 {#1059 #items: array:2 [ 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: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 {#1062 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "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 {#1066 #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" => 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 {#1067 #items: array:3 [ 0 => App\Models\Term {#1076 #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 {#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" => 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 {#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" => 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 {#1073 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Term {#1063 #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 {#1068 #items: array:1 [ 0 => 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" => 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 {#1069 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1071 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1087 #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 {#1080 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1079 #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 {#1084 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Term {#1083 #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 {#1059} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1066} "field_author" => Illuminate\Database\Eloquent\Collection {#1067} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1073} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1074} "field_country" => Illuminate\Database\Eloquent\Collection {#1068} "field_city" => Illuminate\Database\Eloquent\Collection {#1069} "field_series" => Illuminate\Database\Eloquent\Collection {#1071} "field_umk" => Illuminate\Database\Eloquent\Collection {#1065} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1088} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1080} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1081} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1079} "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 {#1084} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1082} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1085} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1091} "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 {#1114 #items: array:4 [ 0 => App\Models\Branch {#1124 #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 {#1125 #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 {#1126 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #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 {#1125} "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 {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #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 {#1128 #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" => 1319340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1129 #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 {#1130 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1129} "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 {#1130} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1131} ] #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 {#1132 #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" => 1319347 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "25. Электрическая емкость. Конденсатор. Энергия электрического поля" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1133 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "180" "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 {#1134 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143 #items: array:1 [ 0 => App\Models\Branch {#1142 #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" => 1319340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144 #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 {#1145 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319340 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое поле" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144} "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 {#1145} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146} ] #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" => 1319347 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "25. Электрическая емкость. Конденсатор. Энергия электрического поля" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1133} "field_page_start" => "180" "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 {#1134} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1143} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Branch {#1136 #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" => 1319349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "184" "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 {#1139 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Branch {#1151 #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" => 1319347 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "25. Электрическая емкость. Конденсатор. Энергия электрического поля" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "180" "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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1142} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319347 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "25. Электрическая емкость. Конденсатор. Энергия электрического поля" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_page_start" => "180" "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #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" => 1319349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "184" "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 {#1139} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1152} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Element {#1105 #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" => 1494085 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1104 #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 {#1101 #items: array:1 [ 0 => App\Models\Term {#1103 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 #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 {#1101} "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 {#1102} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099} "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" => "1319693" "type" => "task" ] "text" => "<p><strong>О07.</strong> В цепи (см. рисунок) емкость каждого конденсатора равна С. Вначале ключ разомкнут, конденсатор 1 заряжен до напряжения $U_0$, остальные конденсаторы не заряжены. Найдите напряжение на каждом из конденсаторов после замыкания ключа.</p><p>☑ $U_1 = 5U_0/8, U_2 = 3U_0/8, U_3 = U_0/4, U_4 = U_5 = U_0/8, U_6 = 0.$</p><p><strong><em>Решение.</em></strong> Обкладки конденсатора 6 соединены накоротко, поэтому у них равные потенциалы. Этот конденсатор не заряжен ($U_6 = 0$) и потому может быть изъят из цепи.</p><p>Тогда $C_{45} = C/2, C_{345} = 3C/2$ и $C_{2345} = \frac{C \cdot 1,5C}{C + 1,5C} = \frac{3}{5}C.$ После замыкания ключа имевшийся на первом конденсаторе заряд $CU_0$ распределится между этим конденсатором и батареей конденсаторов 2-3-4-5, так что $CU_0 = (C + C_{2345})U_1$, откуда $U_1 = 5U_0/8.$ Заряд батареи 2-3-4-5 (и конденсатора 2) равен $C_{2345}U_1 = 3CU_0/8.$</p><p>Следовательно, $U_2 = q_2/C = 3U_0/8, U_3 = U_1 - U_2 = U_0/4$ и $U_4 = U_5 = U_0/8.$</p>" "img" => array:2 [ 0 => array:5 [ "name" => "107-1.jpg" "alt" => null "width" => "1388" "height" => 640 "path" => "/media/fizika_10/gelfgat-z/0-olimp/107-1.webp?ts=1756251262" ] 1 => array:5 [ "name" => "107-2.jpg" "alt" => null "width" => "1299" "height" => 611 "path" => "/media/fizika_10/gelfgat-z/0-olimp/107-2.webp?ts=1756251262" ] ] ] #original: array:7 [ "id" => 1494085 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1319693" "type" => "task" ] "text" => "<p><strong>О07.</strong> В цепи (см. рисунок) емкость каждого конденсатора равна С. Вначале ключ разомкнут, конденсатор 1 заряжен до напряжения $U_0$, остальные конденсаторы не заряжены. Найдите напряжение на каждом из конденсаторов после замыкания ключа.</p><p>☑ $U_1 = 5U_0/8, U_2 = 3U_0/8, U_3 = U_0/4, U_4 = U_5 = U_0/8, U_6 = 0.$</p><p><strong><em>Решение.</em></strong> Обкладки конденсатора 6 соединены накоротко, поэтому у них равные потенциалы. Этот конденсатор не заряжен ($U_6 = 0$) и потому может быть изъят из цепи.</p><p>Тогда $C_{45} = C/2, C_{345} = 3C/2$ и $C_{2345} = \frac{C \cdot 1,5C}{C + 1,5C} = \frac{3}{5}C.$ После замыкания ключа имевшийся на первом конденсаторе заряд $CU_0$ распределится между этим конденсатором и батареей конденсаторов 2-3-4-5, так что $CU_0 = (C + C_{2345})U_1$, откуда $U_1 = 5U_0/8.$ Заряд батареи 2-3-4-5 (и конденсатора 2) равен $C_{2345}U_1 = 3CU_0/8.$</p><p>Следовательно, $U_2 = q_2/C = 3U_0/8, U_3 = U_1 - U_2 = U_0/4$ и $U_4 = U_5 = U_0/8.$</p>" "img" => array:2 [ 0 => array:5 [ "name" => "107-1.jpg" "alt" => null "width" => "1388" "height" => 640 "path" => "/media/fizika_10/gelfgat-z/0-olimp/107-1.webp?ts=1756251262" ] 1 => array:5 [ "name" => "107-2.jpg" "alt" => null "width" => "1299" "height" => 611 "path" => "/media/fizika_10/gelfgat-z/0-olimp/107-2.webp?ts=1756251262" ] ] ] #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 {#1097 #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" => 1691642 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Edition {#1098 #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 {#1093 #items: array:1 [ 0 => App\Models\Term {#1096 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092 #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 {#1093} "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 {#1094} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "1319693" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Емкость каждого конденсатора: $C_1 = C_2 = C_3 = C_4 = C_5 = C_6 = C$</p><p>Начальное напряжение на конденсаторе 1: $U_{1, \text{нач}} = U_0$</p><p>Начальное напряжение на остальных конденсаторах: $U_{2, \text{нач}} = U_{3, \text{нач}} = U_{4, \text{нач}} = U_{5, \text{нач}} = U_{6, \text{нач}} = 0$</p><p><strong>Найти:</strong></p><p>Напряжения на каждом конденсаторе после замыкания ключа: $U_1, U_2, U_3, U_4, U_5, U_6$</p><p><strong>Решение:</strong></p><p>После замыкания ключа, обкладки конденсатора 6 оказываются соединенными проводником, то есть он закорочен. Разность потенциалов, а следовательно и напряжение на нем, равно нулю. Заряд на этом конденсаторе также равен нулю. Поэтому для дальнейшего анализа конденсатор 6 можно исключить из схемы.</p><p>$U_6 = 0$</p><p>Найдем эквивалентную емкость остальной части цепи, к которой подключается конденсатор 1. Будем сворачивать схему, начиная с самого дальнего участка.</p><p>Конденсаторы 4 и 5 соединены последовательно. Их общая емкость $C_{45}$:</p><p>$\frac{1}{C_{45}} = \frac{1}{C_4} + \frac{1}{C_5} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C} \Rightarrow C_{45} = \frac{C}{2}$</p><p>Этот блок (4-5) соединен параллельно с конденсатором 3. Их общая емкость $C_{345}$:</p><p>$C_{345} = C_3 + C_{45} = C + \frac{C}{2} = \frac{3C}{2}$</p><p>Полученный блок (3-4-5) соединен последовательно с конденсатором 2. Их общая емкость $C_{2345}$:</p><p>$\frac{1}{C_{2345}} = \frac{1}{C_2} + \frac{1}{C_{345}} = \frac{1}{C} + \frac{1}{3C/2} = \frac{1}{C} + \frac{2}{3C} = \frac{3+2}{3C} = \frac{5}{3C} \Rightarrow C_{2345} = \frac{3C}{5}$</p><p>После замыкания ключа конденсатор 1 оказывается соединенным параллельно с блоком конденсаторов 2-3-4-5. Изначально заряд был только на конденсаторе 1 и равнялся $Q_0 = C_1 U_0 = CU_0$. Этот заряд перераспределяется между конденсатором 1 и эквивалентным конденсатором $C_{2345}$.</p><p>По закону сохранения заряда, суммарный заряд $Q_0$ сохранится. Общая емкость параллельно соединенных $C_1$ и $C_{2345}$ равна:</p><p>$C_{общ} = C_1 + C_{2345} = C + \frac{3C}{5} = \frac{8C}{5}$</p><p>Установившееся напряжение $U_1$ на конденсаторе 1 (и на всем блоке 2-3-4-5) будет равно:</p><p>$U_1 = \frac{Q_0}{C_{общ}} = \frac{CU_0}{8C/5} = \frac{5}{8}U_0$</p><p>Теперь найдем напряжения на остальных конденсаторах, зная напряжение на всей группе $U_{2345} = U_1 = \frac{5}{8}U_0$.</p><p>Заряд, прошедший через блок 2-3-4-5, равен:</p><p>$q_{2345} = C_{2345} \cdot U_1 = \frac{3C}{5} \cdot \frac{5U_0}{8} = \frac{3CU_0}{8}$</p><p>Так как $C_2$ и $C_{345}$ соединены последовательно, их заряды равны $q_2 = q_{345} = q_{2345}$. Напряжение на конденсаторе 2:</p><p>$U_2 = \frac{q_2}{C_2} = \frac{3CU_0/8}{C} = \frac{3}{8}U_0$</p><p>Напряжение на блоке 3-4-5:</p><p>$U_{345} = \frac{q_{345}}{C_{345}} = \frac{3CU_0/8}{3C/2} = \frac{2U_0}{8} = \frac{1}{4}U_0$</p><p>(Проверка: $U_2 + U_{345} = \frac{3}{8}U_0 + \frac{1}{4}U_0 = \frac{3+2}{8}U_0 = \frac{5}{8}U_0 = U_1$, что верно).</p><p>Конденсатор $C_3$ соединен параллельно блоку 4-5, поэтому напряжение на нем равно напряжению на всем блоке 3-4-5:</p><p>$U_3 = U_{345} = \frac{1}{4}U_0$</p><p>Конденсаторы $C_4$ и $C_5$ соединены последовательно и имеют одинаковую емкость. Значит, напряжение $U_{345}$ делится между ними поровну:</p><p>$U_4 = U_5 = \frac{U_{345}}{2} = \frac{U_0/4}{2} = \frac{1}{8}U_0$</p><p><strong>Ответ:</strong></p><p>$U_1 = \frac{5}{8} U_0$, $U_2 = \frac{3}{8} U_0$, $U_3 = \frac{1}{4} U_0$, $U_4 = \frac{1}{8} U_0$, $U_5 = \frac{1}{8} U_0$, $U_6 = 0$.</p>" ] #original: array:6 [ "id" => 1691642 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052} "task" => array:2 [ "refs" => "1319693" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Емкость каждого конденсатора: $C_1 = C_2 = C_3 = C_4 = C_5 = C_6 = C$</p><p>Начальное напряжение на конденсаторе 1: $U_{1, \text{нач}} = U_0$</p><p>Начальное напряжение на остальных конденсаторах: $U_{2, \text{нач}} = U_{3, \text{нач}} = U_{4, \text{нач}} = U_{5, \text{нач}} = U_{6, \text{нач}} = 0$</p><p><strong>Найти:</strong></p><p>Напряжения на каждом конденсаторе после замыкания ключа: $U_1, U_2, U_3, U_4, U_5, U_6$</p><p><strong>Решение:</strong></p><p>После замыкания ключа, обкладки конденсатора 6 оказываются соединенными проводником, то есть он закорочен. Разность потенциалов, а следовательно и напряжение на нем, равно нулю. Заряд на этом конденсаторе также равен нулю. Поэтому для дальнейшего анализа конденсатор 6 можно исключить из схемы.</p><p>$U_6 = 0$</p><p>Найдем эквивалентную емкость остальной части цепи, к которой подключается конденсатор 1. Будем сворачивать схему, начиная с самого дальнего участка.</p><p>Конденсаторы 4 и 5 соединены последовательно. Их общая емкость $C_{45}$:</p><p>$\frac{1}{C_{45}} = \frac{1}{C_4} + \frac{1}{C_5} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C} \Rightarrow C_{45} = \frac{C}{2}$</p><p>Этот блок (4-5) соединен параллельно с конденсатором 3. Их общая емкость $C_{345}$:</p><p>$C_{345} = C_3 + C_{45} = C + \frac{C}{2} = \frac{3C}{2}$</p><p>Полученный блок (3-4-5) соединен последовательно с конденсатором 2. Их общая емкость $C_{2345}$:</p><p>$\frac{1}{C_{2345}} = \frac{1}{C_2} + \frac{1}{C_{345}} = \frac{1}{C} + \frac{1}{3C/2} = \frac{1}{C} + \frac{2}{3C} = \frac{3+2}{3C} = \frac{5}{3C} \Rightarrow C_{2345} = \frac{3C}{5}$</p><p>После замыкания ключа конденсатор 1 оказывается соединенным параллельно с блоком конденсаторов 2-3-4-5. Изначально заряд был только на конденсаторе 1 и равнялся $Q_0 = C_1 U_0 = CU_0$. Этот заряд перераспределяется между конденсатором 1 и эквивалентным конденсатором $C_{2345}$.</p><p>По закону сохранения заряда, суммарный заряд $Q_0$ сохранится. Общая емкость параллельно соединенных $C_1$ и $C_{2345}$ равна:</p><p>$C_{общ} = C_1 + C_{2345} = C + \frac{3C}{5} = \frac{8C}{5}$</p><p>Установившееся напряжение $U_1$ на конденсаторе 1 (и на всем блоке 2-3-4-5) будет равно:</p><p>$U_1 = \frac{Q_0}{C_{общ}} = \frac{CU_0}{8C/5} = \frac{5}{8}U_0$</p><p>Теперь найдем напряжения на остальных конденсаторах, зная напряжение на всей группе $U_{2345} = U_1 = \frac{5}{8}U_0$.</p><p>Заряд, прошедший через блок 2-3-4-5, равен:</p><p>$q_{2345} = C_{2345} \cdot U_1 = \frac{3C}{5} \cdot \frac{5U_0}{8} = \frac{3CU_0}{8}$</p><p>Так как $C_2$ и $C_{345}$ соединены последовательно, их заряды равны $q_2 = q_{345} = q_{2345}$. Напряжение на конденсаторе 2:</p><p>$U_2 = \frac{q_2}{C_2} = \frac{3CU_0/8}{C} = \frac{3}{8}U_0$</p><p>Напряжение на блоке 3-4-5:</p><p>$U_{345} = \frac{q_{345}}{C_{345}} = \frac{3CU_0/8}{3C/2} = \frac{2U_0}{8} = \frac{1}{4}U_0$</p><p>(Проверка: $U_2 + U_{345} = \frac{3}{8}U_0 + \frac{1}{4}U_0 = \frac{3+2}{8}U_0 = \frac{5}{8}U_0 = U_1$, что верно).</p><p>Конденсатор $C_3$ соединен параллельно блоку 4-5, поэтому напряжение на нем равно напряжению на всем блоке 3-4-5:</p><p>$U_3 = U_{345} = \frac{1}{4}U_0$</p><p>Конденсаторы $C_4$ и $C_5$ соединены последовательно и имеют одинаковую емкость. Значит, напряжение $U_{345}$ делится между ними поровну:</p><p>$U_4 = U_5 = \frac{U_{345}}{2} = \frac{U_0/4}{2} = \frac{1}{8}U_0$</p><p><strong>Ответ:</strong></p><p>$U_1 = \frac{5}{8} U_0$, $U_2 = \frac{3}{8} U_0$, $U_3 = \frac{1}{4} U_0$, $U_4 = \frac{1}{8} U_0$, $U_5 = \frac{1}{8} U_0$, $U_6 = 0$.</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" => "1319694" "type" => "task" ] "previous" => array:2 [ "refs" => "1319692" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1110 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#casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№107 (с. 186)
Условие. №107 (с. 186)
скриншот условия
О07. В цепи (см. рисунок) емкость каждого конденсатора равна С. Вначале ключ разомкнут, конденсатор 1 заряжен до напряжения $U_0$, остальные конденсаторы не заряжены. Найдите напряжение на каждом из конденсаторов после замыкания ключа.
☑ $U_1 = 5U_0/8, U_2 = 3U_0/8, U_3 = U_0/4, U_4 = U_5 = U_0/8, U_6 = 0.$
Решение. Обкладки конденсатора 6 соединены накоротко, поэтому у них равные потенциалы. Этот конденсатор не заряжен ($U_6 = 0$) и потому может быть изъят из цепи.
Тогда $C_{45} = C/2, C_{345} = 3C/2$ и $C_{2345} = \frac{C \cdot 1,5C}{C + 1,5C} = \frac{3}{5}C.$ После замыкания ключа имевшийся на первом конденсаторе заряд $CU_0$ распределится между этим конденсатором и батареей конденсаторов 2-3-4-5, так что $CU_0 = (C + C_{2345})U_1$, откуда $U_1 = 5U_0/8.$ Заряд батареи 2-3-4-5 (и конденсатора 2) равен $C_{2345}U_1 = 3CU_0/8.$
Следовательно, $U_2 = q_2/C = 3U_0/8, U_3 = U_1 - U_2 = U_0/4$ и $U_4 = U_5 = U_0/8.$
Решение. №107 (с. 186)
Дано:
Емкость каждого конденсатора: $C_1 = C_2 = C_3 = C_4 = C_5 = C_6 = C$
Начальное напряжение на конденсаторе 1: $U_{1, \text{нач}} = U_0$
Начальное напряжение на остальных конденсаторах: $U_{2, \text{нач}} = U_{3, \text{нач}} = U_{4, \text{нач}} = U_{5, \text{нач}} = U_{6, \text{нач}} = 0$
Найти:
Напряжения на каждом конденсаторе после замыкания ключа: $U_1, U_2, U_3, U_4, U_5, U_6$
Решение:
После замыкания ключа, обкладки конденсатора 6 оказываются соединенными проводником, то есть он закорочен. Разность потенциалов, а следовательно и напряжение на нем, равно нулю. Заряд на этом конденсаторе также равен нулю. Поэтому для дальнейшего анализа конденсатор 6 можно исключить из схемы.
$U_6 = 0$
Найдем эквивалентную емкость остальной части цепи, к которой подключается конденсатор 1. Будем сворачивать схему, начиная с самого дальнего участка.
Конденсаторы 4 и 5 соединены последовательно. Их общая емкость $C_{45}$:
$\frac{1}{C_{45}} = \frac{1}{C_4} + \frac{1}{C_5} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C} \Rightarrow C_{45} = \frac{C}{2}$
Этот блок (4-5) соединен параллельно с конденсатором 3. Их общая емкость $C_{345}$:
$C_{345} = C_3 + C_{45} = C + \frac{C}{2} = \frac{3C}{2}$
Полученный блок (3-4-5) соединен последовательно с конденсатором 2. Их общая емкость $C_{2345}$:
$\frac{1}{C_{2345}} = \frac{1}{C_2} + \frac{1}{C_{345}} = \frac{1}{C} + \frac{1}{3C/2} = \frac{1}{C} + \frac{2}{3C} = \frac{3+2}{3C} = \frac{5}{3C} \Rightarrow C_{2345} = \frac{3C}{5}$
После замыкания ключа конденсатор 1 оказывается соединенным параллельно с блоком конденсаторов 2-3-4-5. Изначально заряд был только на конденсаторе 1 и равнялся $Q_0 = C_1 U_0 = CU_0$. Этот заряд перераспределяется между конденсатором 1 и эквивалентным конденсатором $C_{2345}$.
По закону сохранения заряда, суммарный заряд $Q_0$ сохранится. Общая емкость параллельно соединенных $C_1$ и $C_{2345}$ равна:
$C_{общ} = C_1 + C_{2345} = C + \frac{3C}{5} = \frac{8C}{5}$
Установившееся напряжение $U_1$ на конденсаторе 1 (и на всем блоке 2-3-4-5) будет равно:
$U_1 = \frac{Q_0}{C_{общ}} = \frac{CU_0}{8C/5} = \frac{5}{8}U_0$
Теперь найдем напряжения на остальных конденсаторах, зная напряжение на всей группе $U_{2345} = U_1 = \frac{5}{8}U_0$.
Заряд, прошедший через блок 2-3-4-5, равен:
$q_{2345} = C_{2345} \cdot U_1 = \frac{3C}{5} \cdot \frac{5U_0}{8} = \frac{3CU_0}{8}$
Так как $C_2$ и $C_{345}$ соединены последовательно, их заряды равны $q_2 = q_{345} = q_{2345}$. Напряжение на конденсаторе 2:
$U_2 = \frac{q_2}{C_2} = \frac{3CU_0/8}{C} = \frac{3}{8}U_0$
Напряжение на блоке 3-4-5:
$U_{345} = \frac{q_{345}}{C_{345}} = \frac{3CU_0/8}{3C/2} = \frac{2U_0}{8} = \frac{1}{4}U_0$
(Проверка: $U_2 + U_{345} = \frac{3}{8}U_0 + \frac{1}{4}U_0 = \frac{3+2}{8}U_0 = \frac{5}{8}U_0 = U_1$, что верно).
Конденсатор $C_3$ соединен параллельно блоку 4-5, поэтому напряжение на нем равно напряжению на всем блоке 3-4-5:
$U_3 = U_{345} = \frac{1}{4}U_0$
Конденсаторы $C_4$ и $C_5$ соединены последовательно и имеют одинаковую емкость. Значит, напряжение $U_{345}$ делится между ними поровну:
$U_4 = U_5 = \frac{U_{345}}{2} = \frac{U_0/4}{2} = \frac{1}{8}U_0$
Ответ:
$U_1 = \frac{5}{8} U_0$, $U_2 = \frac{3}{8} U_0$, $U_3 = \frac{1}{4} U_0$, $U_4 = \frac{1}{8} U_0$, $U_5 = \frac{1}{8} U_0$, $U_6 = 0$.
Другие задания:
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