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Номер 6.6, страница 30 - 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 6.6, страница 30.
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" => 1460229 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #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 {#1039 #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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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 {#1041 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "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 {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "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 {#1070 #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 {#1039} "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 {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:2 [ 0 => App\Models\Element {#1083 #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" => 1753727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1084 #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 {#1086 #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 {#1087 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089 #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 {#1086} "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 {#1087} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089} "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" => "1460229" "type" => "task" ] "text" => "<p><strong>6.6</strong> Длину вольфрамовой проволоки увеличили вытягиванием в 1,4 раза, при этом её диаметр уменьшился в 1,6 раза. Во сколько раз и как изменилось сопротивление проволоки?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1759" "height" => 253 "path" => "/media/fizika_08/artemenkov-zd/0-06/6-1.webp?ts=1760701760" ] ] ] #original: array:7 [ "id" => 1753727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1460229" "type" => "task" ] "text" => "<p><strong>6.6</strong> Длину вольфрамовой проволоки увеличили вытягиванием в 1,4 раза, при этом её диаметр уменьшился в 1,6 раза. Во сколько раз и как изменилось сопротивление проволоки?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1759" "height" => 253 "path" => "/media/fizika_08/artemenkov-zd/0-06/6-1.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 {#1090 #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" => 1821834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1091 #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 {#1094 #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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 #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 {#1094} "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 {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097} "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" => "1460229" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$ \frac{L_2}{L_1} = 1.4 $<br>$ \frac{d_1}{d_2} = 1.6 $</p><p><strong>Найти:</strong></p><p>$ \frac{R_2}{R_1} $ - ?</p><p><strong>Решение:</strong></p><p>Сопротивление проводника $\text{R}$ определяется по формуле: $ R = \rho \frac{L}{S} $, где $ \rho $ — удельное сопротивление материала (в данном случае вольфрама, оно не изменяется), $ L $ — длина проводника, $ S $ — площадь поперечного сечения.</p><p>Площадь поперечного сечения круглого провода выражается через его диаметр $ d $ по формуле: $ S = \frac{\pi d^2}{4} $.</p><p>Подставив выражение для площади в формулу сопротивления, получим зависимость сопротивления от длины и диаметра:</p><p>$ R = \rho \frac{L}{\frac{\pi d^2}{4}} = \frac{4 \rho L}{\pi d^2} $</p><p>Запишем выражения для начального сопротивления $ R_1 $ (до вытягивания) и конечного сопротивления $ R_2 $ (после вытягивания):</p><p>$ R_1 = \frac{4 \rho L_1}{\pi d_1^2} $</p><p>$ R_2 = \frac{4 \rho L_2}{\pi d_2^2} $</p><p>Чтобы найти, во сколько раз изменилось сопротивление, найдем отношение $ \frac{R_2}{R_1} $:</p><p>$ \frac{R_2}{R_1} = \frac{\frac{4 \rho L_2}{\pi d_2^2}}{\frac{4 \rho L_1}{\pi d_1^2}} = \frac{L_2}{L_1} \cdot \frac{d_1^2}{d_2^2} = \frac{L_2}{L_1} \cdot (\frac{d_1}{d_2})^2 $</p><p>Подставим в полученное выражение числовые значения из условия задачи: длина увеличилась в 1,4 раза ($ \frac{L_2}{L_1} = 1.4 $), а диаметр уменьшился в 1,6 раза ($ \frac{d_1}{d_2} = 1.6 $).</p><p>$ \frac{R_2}{R_1} = 1.4 \cdot (1.6)^2 $</p><p>Выполним вычисления:</p><p>$ \frac{R_2}{R_1} = 1.4 \cdot 2.56 = 3.584 $</p><p>Поскольку полученное отношение больше единицы, сопротивление проволоки увеличилось.</p><p><strong>Ответ:</strong> сопротивление проволоки увеличилось в 3,584 раза.</p>" ] #original: array:6 [ "id" => 1821834 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1460229" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$ \frac{L_2}{L_1} = 1.4 $<br>$ \frac{d_1}{d_2} = 1.6 $</p><p><strong>Найти:</strong></p><p>$ \frac{R_2}{R_1} $ - ?</p><p><strong>Решение:</strong></p><p>Сопротивление проводника $\text{R}$ определяется по формуле: $ R = \rho \frac{L}{S} $, где $ \rho $ — удельное сопротивление материала (в данном случае вольфрама, оно не изменяется), $ L $ — длина проводника, $ S $ — площадь поперечного сечения.</p><p>Площадь поперечного сечения круглого провода выражается через его диаметр $ d $ по формуле: $ S = \frac{\pi d^2}{4} $.</p><p>Подставив выражение для площади в формулу сопротивления, получим зависимость сопротивления от длины и диаметра:</p><p>$ R = \rho \frac{L}{\frac{\pi d^2}{4}} = \frac{4 \rho L}{\pi d^2} $</p><p>Запишем выражения для начального сопротивления $ R_1 $ (до вытягивания) и конечного сопротивления $ R_2 $ (после вытягивания):</p><p>$ R_1 = \frac{4 \rho L_1}{\pi d_1^2} $</p><p>$ R_2 = \frac{4 \rho L_2}{\pi d_2^2} $</p><p>Чтобы найти, во сколько раз изменилось сопротивление, найдем отношение $ \frac{R_2}{R_1} $:</p><p>$ \frac{R_2}{R_1} = \frac{\frac{4 \rho L_2}{\pi d_2^2}}{\frac{4 \rho L_1}{\pi d_1^2}} = \frac{L_2}{L_1} \cdot \frac{d_1^2}{d_2^2} = \frac{L_2}{L_1} \cdot (\frac{d_1}{d_2})^2 $</p><p>Подставим в полученное выражение числовые значения из условия задачи: длина увеличилась в 1,4 раза ($ \frac{L_2}{L_1} = 1.4 $), а диаметр уменьшился в 1,6 раза ($ \frac{d_1}{d_2} = 1.6 $).</p><p>$ \frac{R_2}{R_1} = 1.4 \cdot (1.6)^2 $</p><p>Выполним вычисления:</p><p>$ \frac{R_2}{R_1} = 1.4 \cdot 2.56 = 3.584 $</p><p>Поскольку полученное отношение больше единицы, сопротивление проволоки увеличилось.</p><p><strong>Ответ:</strong> сопротивление проволоки увеличилось в 3,584 раза.</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" => "1460230" "type" => "task" ] "previous" => array:2 [ "refs" => "1460228" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1080 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1079 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1077 #items: array:3 [ 0 => App\Models\Term {#1098 #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 {#1099 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false 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} 2 => 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: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 {#1102 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1104 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 [ 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#dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Term {#1106 #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 {#1107 #items: array:1 [ 0 => App\Models\Term {#1108 #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" => 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Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Term {#1110 #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 {#1111 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Term {#1101} ] #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 {#1116 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Term {#1120 #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 {#1072} "field_class" => Illuminate\Database\Eloquent\Collection {#1082} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "field_author" => Illuminate\Database\Eloquent\Collection {#1077} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1102} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_country" => Illuminate\Database\Eloquent\Collection {#1105} "field_city" => Illuminate\Database\Eloquent\Collection {#1107} "field_series" => Illuminate\Database\Eloquent\Collection {#1109} "field_umk" => Illuminate\Database\Eloquent\Collection {#1111} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115} "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 {#1116} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119} "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 {#1128 #items: array:1 [ 0 => App\Models\BookPage {#1127 #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" => 1462327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-30" "field_display_title" => "30" "field_folder" => "1" "field_image_name" => "30" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1080} ] #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 {#1131 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Element {#1140 #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" => 1753888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1753888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "book_page" => array:2 [ "refs" => "1462327" "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" => "1462328" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462326" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:9 [ 0 => App\Models\Task {#1241 #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" => 1460224 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-1" "field_display_title" => "6.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242 #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 {#1243 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460225" "type" => "task" ] "previous" => array:2 [ "refs" => "1460223" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460224 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-1" "field_display_title" => "6.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242} "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 {#1243} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245} "content" => Illuminate\Database\Eloquent\Collection {#1247} "next" => array:2 [ "refs" => "1460225" "type" => "task" ] "previous" => array:2 [ "refs" => "1460223" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1253} "page" => array:2 [ "refs" => "1462327" "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 {#1248 #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" => 1460225 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-2" "field_display_title" => "6.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 #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 {#1255 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460226" "type" => "task" ] "previous" => array:2 [ "refs" => "1460224" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460225 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-2" "field_display_title" => "6.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246} "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 {#1255} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1249} "content" => Illuminate\Database\Eloquent\Collection {#1250} "next" => array:2 [ "refs" => "1460226" "type" => "task" ] "previous" => array:2 [ "refs" => "1460224" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1265} "page" => array:2 [ "refs" => "1462327" "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 {#1260 #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" => 1460226 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-3" "field_display_title" => "6.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252 #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 {#1267 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460227" "type" => "task" ] "previous" => array:2 [ "refs" => "1460225" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1285 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460226 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-3" "field_display_title" => "6.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1252} "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 {#1267} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261} "content" => Illuminate\Database\Eloquent\Collection {#1280} "next" => array:2 [ "refs" => "1460227" "type" => "task" ] "previous" => array:2 [ "refs" => "1460225" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1285} "page" => array:2 [ "refs" => "1462327" "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 => "*" ] } 3 => App\Models\Task {#1264 #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" => 1460227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-4" "field_display_title" => "6.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272 #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 {#1262 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460228" "type" => "task" ] "previous" => array:2 [ "refs" => "1460226" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460227 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-4" "field_display_title" => "6.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272} "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 {#1262} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276} "content" => Illuminate\Database\Eloquent\Collection {#1273} "next" => array:2 [ "refs" => "1460228" "type" => "task" ] "previous" => array:2 [ "refs" => "1460226" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1281} "page" => array:2 [ "refs" => "1462327" "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 => "*" ] } 4 => App\Models\Task {#1274 #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" => 1460228 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-5" "field_display_title" => "6.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275 #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 {#1282 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460229" "type" => "task" ] "previous" => array:2 [ "refs" => "1460227" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1301 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460228 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-5" "field_display_title" => "6.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1275} "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 {#1282} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1279} "content" => Illuminate\Database\Eloquent\Collection {#1278} "next" => array:2 [ "refs" => "1460229" "type" => "task" ] "previous" => array:2 [ "refs" => "1460227" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1301} "page" => array:2 [ "refs" => "1462327" "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 => "*" ] } 5 => App\Models\Task {#1296 #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" => 1460229 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-6" "field_display_title" => "6.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1283 #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 {#1303 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460230" "type" => "task" ] "previous" => array:2 [ "refs" => "1460228" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1298 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462327" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460229 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"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 => App\Models\Task {#1308 #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" => 1460230 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-7" "field_display_title" => "6.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1309 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null 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#relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Task {#1315 #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" => 1460231 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "30" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/06-8" "field_display_title" => "6.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1313 …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 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№6.6 (с. 30)
Условие. №6.6 (с. 30)
скриншот условия
6.6 Длину вольфрамовой проволоки увеличили вытягиванием в 1,4 раза, при этом её диаметр уменьшился в 1,6 раза. Во сколько раз и как изменилось сопротивление проволоки?
Решение. №6.6 (с. 30)
Дано:
$ \frac{L_2}{L_1} = 1.4 $
$ \frac{d_1}{d_2} = 1.6 $
Найти:
$ \frac{R_2}{R_1} $ - ?
Решение:
Сопротивление проводника $\text{R}$ определяется по формуле: $ R = \rho \frac{L}{S} $, где $ \rho $ — удельное сопротивление материала (в данном случае вольфрама, оно не изменяется), $ L $ — длина проводника, $ S $ — площадь поперечного сечения.
Площадь поперечного сечения круглого провода выражается через его диаметр $ d $ по формуле: $ S = \frac{\pi d^2}{4} $.
Подставив выражение для площади в формулу сопротивления, получим зависимость сопротивления от длины и диаметра:
$ R = \rho \frac{L}{\frac{\pi d^2}{4}} = \frac{4 \rho L}{\pi d^2} $
Запишем выражения для начального сопротивления $ R_1 $ (до вытягивания) и конечного сопротивления $ R_2 $ (после вытягивания):
$ R_1 = \frac{4 \rho L_1}{\pi d_1^2} $
$ R_2 = \frac{4 \rho L_2}{\pi d_2^2} $
Чтобы найти, во сколько раз изменилось сопротивление, найдем отношение $ \frac{R_2}{R_1} $:
$ \frac{R_2}{R_1} = \frac{\frac{4 \rho L_2}{\pi d_2^2}}{\frac{4 \rho L_1}{\pi d_1^2}} = \frac{L_2}{L_1} \cdot \frac{d_1^2}{d_2^2} = \frac{L_2}{L_1} \cdot (\frac{d_1}{d_2})^2 $
Подставим в полученное выражение числовые значения из условия задачи: длина увеличилась в 1,4 раза ($ \frac{L_2}{L_1} = 1.4 $), а диаметр уменьшился в 1,6 раза ($ \frac{d_1}{d_2} = 1.6 $).
$ \frac{R_2}{R_1} = 1.4 \cdot (1.6)^2 $
Выполним вычисления:
$ \frac{R_2}{R_1} = 1.4 \cdot 2.56 = 3.584 $
Поскольку полученное отношение больше единицы, сопротивление проволоки увеличилось.
Ответ: сопротивление проволоки увеличилось в 3,584 раза.
Другие задания:
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