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Номер 6.18, страница 32 - гдз по физике 8 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2010 - 2026
Цвет обложки: фиолетовый
ISBN: 978-5-09-046040-8
Популярные ГДЗ в 8 классе
VI. Расчёт характеристик электрических цепей - номер 6.18, страница 32.
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" => 1460241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-18" "field_display_title" => "6.18" "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" => 1460049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "VI. Расчёт характеристик электрических цепей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "30" "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 {#1033 #items: array:1 [ 0 => App\Models\Book {#1030 #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" => 1646 "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 {#1032 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1035 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1032} "field_class" => Illuminate\Database\Eloquent\Collection {#1035} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1037} "field_author" => Illuminate\Database\Eloquent\Collection {#1039} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1043} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1044} "field_country" => Illuminate\Database\Eloquent\Collection {#1046} "field_city" => Illuminate\Database\Eloquent\Collection {#1048} "field_series" => Illuminate\Database\Eloquent\Collection {#1050} "field_umk" => Illuminate\Database\Eloquent\Collection {#1052} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 {#1062 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1460049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "VI. Расчёт характеристик электрических цепей" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "30" "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 {#1033} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #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 {#1063 #items: array:1 [ 0 => App\Models\Branch {#1023} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:2 [ 0 => App\Models\Element {#1065 #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" => 1753739 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Edition {#1067 #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" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1070 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1068} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1070} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1071} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1072} "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" => "1460241" "type" => "task" ] "text" => "<p><strong>6.18</strong> Однородный кусок проволоки сопротивлением 135 Ом разрезали на три равные части. Полученные куски соединили параллельно. Определите сопротивление этого соединения.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1759" "height" => 271 "path" => "/media/fizika_08/artemenkov-zd/0-06/18-1.webp?ts=1760701760" ] ] ] #original: array:7 [ "id" => 1753739 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1066} "task" => array:2 [ "refs" => "1460241" "type" => "task" ] "text" => "<p><strong>6.18</strong> Однородный кусок проволоки сопротивлением 135 Ом разрезали на три равные части. Полученные куски соединили параллельно. Определите сопротивление этого соединения.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "18-1.jpg" "alt" => null "width" => "1759" "height" => 271 "path" => "/media/fizika_08/artemenkov-zd/0-06/18-1.webp?ts=1760701760" ] ] ] #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 {#1073 #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" => 1821846 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Edition {#1075 #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" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1078 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1078} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080} "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" => "1460241" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Общее сопротивление проволоки $R_{общ} = 135$ Ом.</p><p>Количество частей $n = 3$.</p><p><strong>Найти:</strong></p><p>Сопротивление параллельного соединения $R_{пар}$.</p><p><strong>Решение:</strong></p><p>Сопротивление однородного проводника прямо пропорционально его длине. Когда мы разрезаем проволоку на три равные части, длина каждой части становится в три раза меньше, а значит и сопротивление каждой части также будет в три раза меньше исходного.</p><p>Найдем сопротивление одного куска проволоки, обозначим его $R_1$:</p><p>$R_1 = \frac{R_{общ}}{n} = \frac{135 \text{ Ом}}{3} = 45 \text{ Ом}$</p><p>Так как все три части одинаковы, то их сопротивления равны:</p><p>$R_1 = R_2 = R_3 = 45 \text{ Ом}$</p><p>При параллельном соединении проводников величина, обратная общему сопротивлению, равна сумме величин, обратных сопротивлениям каждого проводника:</p><p>$\frac{1}{R_{пар}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$</p><p>Так как сопротивления всех трех частей равны ($R_1 = R_2 = R_3$), можно использовать упрощенную формулу для $\text{n}$ одинаковых сопротивлений, соединенных параллельно:</p><p>$R_{пар} = \frac{R_1}{n}$</p><p>Подставим значения:</p><p>$R_{пар} = \frac{45 \text{ Ом}}{3} = 15 \text{ Ом}$</p><p><strong>Ответ:</strong> 15 Ом.</p>" ] #original: array:6 [ "id" => 1821846 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074} "task" => array:2 [ "refs" => "1460241" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Общее сопротивление проволоки $R_{общ} = 135$ Ом.</p><p>Количество частей $n = 3$.</p><p><strong>Найти:</strong></p><p>Сопротивление параллельного соединения $R_{пар}$.</p><p><strong>Решение:</strong></p><p>Сопротивление однородного проводника прямо пропорционально его длине. Когда мы разрезаем проволоку на три равные части, длина каждой части становится в три раза меньше, а значит и сопротивление каждой части также будет в три раза меньше исходного.</p><p>Найдем сопротивление одного куска проволоки, обозначим его $R_1$:</p><p>$R_1 = \frac{R_{общ}}{n} = \frac{135 \text{ Ом}}{3} = 45 \text{ Ом}$</p><p>Так как все три части одинаковы, то их сопротивления равны:</p><p>$R_1 = R_2 = R_3 = 45 \text{ Ом}$</p><p>При параллельном соединении проводников величина, обратная общему сопротивлению, равна сумме величин, обратных сопротивлениям каждого проводника:</p><p>$\frac{1}{R_{пар}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$</p><p>Так как сопротивления всех трех частей равны ($R_1 = R_2 = R_3$), можно использовать упрощенную формулу для $\text{n}$ одинаковых сопротивлений, соединенных параллельно:</p><p>$R_{пар} = \frac{R_1}{n}$</p><p>Подставим значения:</p><p>$R_{пар} = \frac{45 \text{ Ом}}{3} = 15 \text{ Ом}$</p><p><strong>Ответ:</strong> 15 Ом.</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" => "1460242" "type" => "task" ] "previous" => array:2 [ "refs" => "1460240" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Book {#1082 #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" => 1646 "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 {#1083 #items: array:1 [ 0 => App\Models\Term {#1084 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1085 #items: array:1 [ 0 => App\Models\Term {#1086 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #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 {#1087 #items: array:1 [ 0 => App\Models\Term {#1088 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1089 #items: array:3 [ 0 => App\Models\Term {#1090 #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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "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 => "*" ] } 1 => App\Models\Term {#1091 #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" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "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 {#1092 #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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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 {#1093 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1095 #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 {#1096 #items: array:1 [ 0 => App\Models\Term {#1097 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1098 #items: array:1 [ 0 => App\Models\Term {#1099 #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 {#1100 #items: array:1 [ 0 => App\Models\Term {#1101 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ 0 => App\Models\Term {#1092} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Term {#1111 #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" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1083} "field_class" => Illuminate\Database\Eloquent\Collection {#1085} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087} "field_author" => Illuminate\Database\Eloquent\Collection {#1089} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1093} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1094} "field_country" => Illuminate\Database\Eloquent\Collection {#1096} "field_city" => Illuminate\Database\Eloquent\Collection {#1098} "field_series" => Illuminate\Database\Eloquent\Collection {#1100} "field_umk" => Illuminate\Database\Eloquent\Collection {#1102} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1103} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1104} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1105} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1106} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1107} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1108} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1109} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1110} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ 0 => App\Models\BookPage {#1115 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1462329 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-32" "field_display_title" => "32" "field_folder" => "1" "field_image_name" => "32" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1119 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Book {#1120 #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" => 1646 "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 {#1121 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1121} "field_class" => Illuminate\Database\Eloquent\Collection {#1123} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1131} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_country" => Illuminate\Database\Eloquent\Collection {#1134} "field_city" => Illuminate\Database\Eloquent\Collection {#1136} "field_series" => Illuminate\Database\Eloquent\Collection {#1138} "field_umk" => Illuminate\Database\Eloquent\Collection {#1140} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1141} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1142} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1143} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 "edition_groups" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1151 #items: array:1 [ 0 => App\Models\Element {#1152 #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" => 1753890 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1753890 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1153} "book_page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1462330" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462328" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:8 [ 0 => App\Models\Task {#1161 #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" => 1460241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-18" "field_display_title" => "6.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ …1] #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 {#1164 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460242" "type" => "task" ] "previous" => array:2 [ "refs" => "1460240" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1212 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-18" "field_display_title" => "6.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1162} "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 {#1164} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1165} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1200} "content" => Illuminate\Database\Eloquent\Collection {#1201} "next" => array:2 [ "refs" => "1460242" "type" => "task" ] "previous" => array:2 [ "refs" => "1460240" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1212} "page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1213 #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" => 1460242 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-19" "field_display_title" => "6.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ …1] #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 {#1215 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460243" "type" => "task" ] "previous" => array:2 [ "refs" => "1460241" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460242 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-19" "field_display_title" => "6.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214} "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 {#1215} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1216} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1217} "content" => Illuminate\Database\Eloquent\Collection {#1218} "next" => array:2 [ "refs" => "1460243" "type" => "task" ] "previous" => array:2 [ "refs" => "1460241" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223} "page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1224 #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" => 1460243 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-20" "field_display_title" => "6.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ …1] #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 {#1226 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460244" "type" => "task" ] "previous" => array:2 [ "refs" => "1460242" …1 ] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460243 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-20" "field_display_title" => "6.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225} "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 {#1226} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1227} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228} "content" => Illuminate\Database\Eloquent\Collection {#1229} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1234 …2} "page" => array:2 [ …2] ] #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\Task {#1235 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1460244 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-21" "field_display_title" => "6.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1236 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1237 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1239 …2} "content" => Illuminate\Database\Eloquent\Collection {#1240 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460244 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-21" "field_display_title" => "6.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1236 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1237 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1238 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1239 …2} "content" => Illuminate\Database\Eloquent\Collection {#1240 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1245 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1246 #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" => 1460245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-22" "field_display_title" => "6.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1247 …2} "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 {#1248 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1250 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1256 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460245 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-22" "field_display_title" => "6.22" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1247 …2} "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 {#1248 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1250 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1256 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1257 #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" => 1460246 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-23" "field_display_title" => "6.23" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …2} "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 {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1262 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1267 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460246 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-23" "field_display_title" => "6.23" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …2} "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 {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1262 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1267 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1268 #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" => 1460247 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-24" "field_display_title" => "6.24" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …2} "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 {#1270 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1271 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1272 …2} "content" => Illuminate\Database\Eloquent\Collection {#1273 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => 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null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1282 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283 …2} "content" => Illuminate\Database\Eloquent\Collection {#1284 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1289 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1460248 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-25" "field_display_title" => "6.25" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1280 …2} "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 {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1282 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1283 …2} "content" => Illuminate\Database\Eloquent\Collection {#1284 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1289 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1462329 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-32" "field_display_title" => "32" "field_folder" => "1" "field_image_name" => "32" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1119} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1114} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1150} "content" => Illuminate\Database\Eloquent\Collection {#1151} "next" => array:2 [ "refs" => "1462330" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462328" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1160} ] #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" => 1460241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "32" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-18" "field_display_title" => "6.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1063} "content" => Illuminate\Database\Eloquent\Collection {#1064} "next" => array:2 [ "refs" => "1460242" "type" => "task" ] "previous" => array:2 [ "refs" => "1460240" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1081} "page" => array:2 [ "refs" => "1462329" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№6.18 (с. 32)
Условие. №6.18 (с. 32)
скриншот условия
6.18 Однородный кусок проволоки сопротивлением 135 Ом разрезали на три равные части. Полученные куски соединили параллельно. Определите сопротивление этого соединения.
Решение. №6.18 (с. 32)
Дано:
Общее сопротивление проволоки $R_{общ} = 135$ Ом.
Количество частей $n = 3$.
Найти:
Сопротивление параллельного соединения $R_{пар}$.
Решение:
Сопротивление однородного проводника прямо пропорционально его длине. Когда мы разрезаем проволоку на три равные части, длина каждой части становится в три раза меньше, а значит и сопротивление каждой части также будет в три раза меньше исходного.
Найдем сопротивление одного куска проволоки, обозначим его $R_1$:
$R_1 = \frac{R_{общ}}{n} = \frac{135 \text{ Ом}}{3} = 45 \text{ Ом}$
Так как все три части одинаковы, то их сопротивления равны:
$R_1 = R_2 = R_3 = 45 \text{ Ом}$
При параллельном соединении проводников величина, обратная общему сопротивлению, равна сумме величин, обратных сопротивлениям каждого проводника:
$\frac{1}{R_{пар}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$
Так как сопротивления всех трех частей равны ($R_1 = R_2 = R_3$), можно использовать упрощенную формулу для $\text{n}$ одинаковых сопротивлений, соединенных параллельно:
$R_{пар} = \frac{R_1}{n}$
Подставим значения:
$R_{пар} = \frac{45 \text{ Ом}}{3} = 15 \text{ Ом}$
Ответ: 15 Ом.
Другие задания:
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ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 8 класс, для упражнения номер 6.18 расположенного на странице 32 к задачнику серии сферы 2010 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №6.18 (с. 32), авторов: Артеменков (Денис Александрович), Ломаченков (Иван Алексеевич), Панебратцев (Юрий Анатольевич), учебного пособия издательства Просвещение.