gdz.top
Номер 16, страница 121 - гдз по физике 8 класс учебник Изергин
Авторы: Изергин Э. Т.
Тип: Учебник
Издательство: Русское слово
Год издания: 2019 - 2026
Цвет обложки: синий
ISBN: 978-5-533-01067-2
Популярные ГДЗ в 8 классе
Глава III. Постоянный электрический ток. Параграф 19. Электрическое сопротивление проводника - номер 16, страница 121.
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" => 1492414 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "121" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/19-16" "field_display_title" => "16" "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" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "95" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #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" => 4168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043} "field_country" => Illuminate\Database\Eloquent\Collection {#1045} "field_city" => Illuminate\Database\Eloquent\Collection {#1047} "field_series" => Illuminate\Database\Eloquent\Collection {#1049} "field_umk" => Illuminate\Database\Eloquent\Collection {#1050} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} "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 {#1061 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "95" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1061} ] #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 {#1062 #items: array:2 [ 0 => App\Models\Branch {#1063 #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" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "95" "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 {#1066 #items: array:1 [ 0 => App\Models\Book {#1067 #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" => 4168 "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 {#1068 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1090 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1093 #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" => 4168 "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 {#1068} "field_class" => Illuminate\Database\Eloquent\Collection {#1070} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072} "field_author" => Illuminate\Database\Eloquent\Collection {#1074} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_country" => Illuminate\Database\Eloquent\Collection {#1079} "field_city" => Illuminate\Database\Eloquent\Collection {#1081} "field_series" => Illuminate\Database\Eloquent\Collection {#1083} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1088} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1089} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1090} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1091} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1092} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1093} "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 {#1095 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_page_start" => "95" "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 {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1095} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1096 #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" => 1492179 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое сопротивление проводника" "field_branch_order" => "19" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 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:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "113" "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 {#1099 #items: array:1 [ 0 => App\Models\Book {#1100 #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" => 4168 "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 {#1101 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1121 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1122 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1123 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1126 #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" => 4168 "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 {#1101} "field_class" => Illuminate\Database\Eloquent\Collection {#1103} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105} "field_author" => Illuminate\Database\Eloquent\Collection {#1107} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1109} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1110} "field_country" => Illuminate\Database\Eloquent\Collection {#1112} "field_city" => Illuminate\Database\Eloquent\Collection {#1114} "field_series" => Illuminate\Database\Eloquent\Collection {#1116} "field_umk" => Illuminate\Database\Eloquent\Collection {#1117} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1118} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1119} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1121} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1122} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "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 {#1123} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1124} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1125} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1126} "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 {#1128 #items: array:1 [ 0 => App\Models\Branch {#1129 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "95" "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 {#1132 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1492175 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Постоянный электрический ток" "field_branch_order" => "III" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_page_start" => "95" "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 {#1132} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1161} ] #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" => 1492179 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электрическое сопротивление проводника" "field_branch_order" => "19" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1097} "field_page_start" => "113" "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 {#1099} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:2 [ 0 => App\Models\Element {#1163 #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" => 1774564 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => App\Models\Edition {#1165 #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" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1166 #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 {#1168 #items: [] …1 } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1166} "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 {#1168 …1} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1170 …2} "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" => "1492414" "type" => "task" ] "text" => "<p><strong>16*.</strong> Используя таблицу 15, составьте несколько различных задач на расчёт электрического сопротивления проводника.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1469" "height" => 289 "path" => "/media/fizika_08/izergin-u/0-19/16-1.webp?ts=1761329210" ] ] ] #original: array:7 [ "id" => 1774564 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1164} "task" => array:2 [ "refs" => "1492414" "type" => "task" ] "text" => "<p><strong>16*.</strong> Используя таблицу 15, составьте несколько различных задач на расчёт электрического сопротивления проводника.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1469" "height" => 289 "path" => "/media/fizika_08/izergin-u/0-19/16-1.webp?ts=1761329210" ] ] ] #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 {#1171 #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" => 1851736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Edition {#1173 #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" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …2} "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 {#1176 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_content_source" => null ] #original: array:21 [ "id" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …2} "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 {#1176 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1178 …2} "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" => "1492414" "type" => "task" ] "text" => "<p>Поскольку таблица 15 не предоставлена, для составления и решения задач будут использоваться стандартные значения удельных электрических сопротивлений некоторых распространенных материалов (при температуре 20 °C), которые будут приводиться в условии каждой задачи.</p><p>Ниже представлены несколько различных задач на расчет электрического сопротивления проводника.</p><p><strong>Задача 1.</strong> Рассчитайте сопротивление медного провода длиной 100 м и площадью поперечного сечения 2 мм².</p><p><strong>Дано:</strong></p><p>$l = 100$ м</p><p>$S = 2$ мм²</p><p>Удельное сопротивление меди, $\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$S = 2 \text{ мм}^2 = 2 \cdot 10^{-6} \text{ м}^2$</p><p>$\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{R}$ - ?</p><p><strong>Решение:</strong></p><p>Формула для расчета сопротивления проводника:</p><p>$R = \rho \frac{l}{S}$</p><p>Подставим значения в системе СИ:</p><p>$R = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м} \cdot \frac{100 \text{ м}}{2 \cdot 10^{-6} \text{ м}^2} = \frac{1,7 \cdot 100}{2} \cdot 10^{-8 - (-6)} \text{ Ом} = 85 \cdot 10^{-2} \text{ Ом} = 0,85 \text{ Ом}$</p><p><strong>Ответ:</strong> 0,85 Ом.</p><p><strong>Задача 2.</strong> Алюминиевый провод имеет сопротивление 5 Ом и площадь поперечного сечения 1 мм². Какова длина этого провода?</p><p><strong>Дано:</strong></p><p>$R = 5$ Ом</p><p>$S = 1$ мм²</p><p>Удельное сопротивление алюминия, $\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$S = 1 \text{ мм}^2 = 1 \cdot 10^{-6} \text{ м}^2$</p><p>$\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{l}$ - ?</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим длину проводника $\text{l}$:</p><p>$l = \frac{R \cdot S}{\rho}$</p><p>Подставим значения в системе СИ:</p><p>$l = \frac{5 \text{ Ом} \cdot 1 \cdot 10^{-6} \text{ м}^2}{2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}} = \frac{5}{2,8} \cdot 10^{-6 - (-8)} \text{ м} \approx 1,786 \cdot 10^2 \text{ м} \approx 178,6 \text{ м}$</p><p><strong>Ответ:</strong> ≈178,6 м.</p><p><strong>Задача 3.</strong> Нагревательный элемент изготовлен из нихромовой проволоки длиной 5,5 м. Его сопротивление составляет 22 Ом. Определите площадь поперечного сечения и диаметр проволоки.</p><p><strong>Дано:</strong></p><p>$l = 5,5$ м</p><p>$R = 22$ Ом</p><p>Удельное сопротивление нихрома, $\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{S}$ - ?, $\text{d}$ - ?</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим площадь поперечного сечения $\text{S}$:</p><p>$S = \frac{\rho \cdot l}{R}$</p><p>Подставим значения в системе СИ:</p><p>$S = \frac{1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м} \cdot 5,5 \text{ м}}{22 \text{ Ом}} = \frac{6,05}{22} \cdot 10^{-6} \text{ м}^2 = 0,275 \cdot 10^{-6} \text{ м}^2$</p><p>Для наглядности переведем площадь в квадратные миллиметры: $S = 0,275 \text{ мм}^2$.</p><p>Площадь поперечного сечения круглого провода связана с его диаметром $\text{d}$ формулой $S = \frac{\pi d^2}{4}$. Выразим диаметр:</p><p>$d = \sqrt{\frac{4S}{\pi}}$</p><p>Подставим значение площади $\text{S}$ в системе СИ:</p><p>$d = \sqrt{\frac{4 \cdot 0,275 \cdot 10^{-6} \text{ м}^2}{\pi}} \approx \sqrt{\frac{1,1 \cdot 10^{-6}}{3,14}} \text{ м} \approx \sqrt{0,35 \cdot 10^{-6}} \text{ м} \approx 0,59 \cdot 10^{-3} \text{ м}$</p><p>Переведем диаметр в миллиметры: $d \approx 0,59$ мм.</p><p><strong>Ответ:</strong> Площадь поперечного сечения $S = 0,275$ мм², диаметр $d \approx 0,59$ мм.</p><p><strong>Задача 4.</strong> Проводник длиной 20 м и площадью поперечного сечения 0,5 мм² имеет сопротивление 1,12 Ом. Определите, из какого материала изготовлен проводник (используя табличные значения удельных сопротивлений).</p><p><strong>Дано:</strong></p><p>$l = 20$ м</p><p>$S = 0,5$ мм²</p><p>$R = 1,12$ Ом</p><p>Перевод в СИ:</p><p>$S = 0,5 \text{ мм}^2 = 0,5 \cdot 10^{-6} \text{ м}^2$</p><p><strong>Найти:</strong></p><p>Материал проводника ($\rho$ - ?)</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим удельное сопротивление $\rho$:</p><p>$\rho = \frac{R \cdot S}{l}$</p><p>Подставим значения в системе СИ:</p><p>$\rho = \frac{1,12 \text{ Ом} \cdot 0,5 \cdot 10^{-6} \text{ м}^2}{20 \text{ м}} = \frac{0,56}{20} \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 0,028 \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p>Сравнив полученное значение с табличными данными ($ \rho_{алюминий} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м} $), делаем вывод, что проводник изготовлен из алюминия.</p><p><strong>Ответ:</strong> Проводник изготовлен из алюминия.</p>" ] #original: array:6 [ "id" => 1851736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172} "task" => array:2 [ "refs" => "1492414" "type" => "task" ] "text" => "<p>Поскольку таблица 15 не предоставлена, для составления и решения задач будут использоваться стандартные значения удельных электрических сопротивлений некоторых распространенных материалов (при температуре 20 °C), которые будут приводиться в условии каждой задачи.</p><p>Ниже представлены несколько различных задач на расчет электрического сопротивления проводника.</p><p><strong>Задача 1.</strong> Рассчитайте сопротивление медного провода длиной 100 м и площадью поперечного сечения 2 мм².</p><p><strong>Дано:</strong></p><p>$l = 100$ м</p><p>$S = 2$ мм²</p><p>Удельное сопротивление меди, $\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$S = 2 \text{ мм}^2 = 2 \cdot 10^{-6} \text{ м}^2$</p><p>$\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{R}$ - ?</p><p><strong>Решение:</strong></p><p>Формула для расчета сопротивления проводника:</p><p>$R = \rho \frac{l}{S}$</p><p>Подставим значения в системе СИ:</p><p>$R = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м} \cdot \frac{100 \text{ м}}{2 \cdot 10^{-6} \text{ м}^2} = \frac{1,7 \cdot 100}{2} \cdot 10^{-8 - (-6)} \text{ Ом} = 85 \cdot 10^{-2} \text{ Ом} = 0,85 \text{ Ом}$</p><p><strong>Ответ:</strong> 0,85 Ом.</p><p><strong>Задача 2.</strong> Алюминиевый провод имеет сопротивление 5 Ом и площадь поперечного сечения 1 мм². Какова длина этого провода?</p><p><strong>Дано:</strong></p><p>$R = 5$ Ом</p><p>$S = 1$ мм²</p><p>Удельное сопротивление алюминия, $\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$S = 1 \text{ мм}^2 = 1 \cdot 10^{-6} \text{ м}^2$</p><p>$\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{l}$ - ?</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим длину проводника $\text{l}$:</p><p>$l = \frac{R \cdot S}{\rho}$</p><p>Подставим значения в системе СИ:</p><p>$l = \frac{5 \text{ Ом} \cdot 1 \cdot 10^{-6} \text{ м}^2}{2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}} = \frac{5}{2,8} \cdot 10^{-6 - (-8)} \text{ м} \approx 1,786 \cdot 10^2 \text{ м} \approx 178,6 \text{ м}$</p><p><strong>Ответ:</strong> ≈178,6 м.</p><p><strong>Задача 3.</strong> Нагревательный элемент изготовлен из нихромовой проволоки длиной 5,5 м. Его сопротивление составляет 22 Ом. Определите площадь поперечного сечения и диаметр проволоки.</p><p><strong>Дано:</strong></p><p>$l = 5,5$ м</p><p>$R = 22$ Ом</p><p>Удельное сопротивление нихрома, $\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$</p><p>Перевод в СИ:</p><p>$\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м}$</p><p><strong>Найти:</strong></p><p>$\text{S}$ - ?, $\text{d}$ - ?</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим площадь поперечного сечения $\text{S}$:</p><p>$S = \frac{\rho \cdot l}{R}$</p><p>Подставим значения в системе СИ:</p><p>$S = \frac{1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м} \cdot 5,5 \text{ м}}{22 \text{ Ом}} = \frac{6,05}{22} \cdot 10^{-6} \text{ м}^2 = 0,275 \cdot 10^{-6} \text{ м}^2$</p><p>Для наглядности переведем площадь в квадратные миллиметры: $S = 0,275 \text{ мм}^2$.</p><p>Площадь поперечного сечения круглого провода связана с его диаметром $\text{d}$ формулой $S = \frac{\pi d^2}{4}$. Выразим диаметр:</p><p>$d = \sqrt{\frac{4S}{\pi}}$</p><p>Подставим значение площади $\text{S}$ в системе СИ:</p><p>$d = \sqrt{\frac{4 \cdot 0,275 \cdot 10^{-6} \text{ м}^2}{\pi}} \approx \sqrt{\frac{1,1 \cdot 10^{-6}}{3,14}} \text{ м} \approx \sqrt{0,35 \cdot 10^{-6}} \text{ м} \approx 0,59 \cdot 10^{-3} \text{ м}$</p><p>Переведем диаметр в миллиметры: $d \approx 0,59$ мм.</p><p><strong>Ответ:</strong> Площадь поперечного сечения $S = 0,275$ мм², диаметр $d \approx 0,59$ мм.</p><p><strong>Задача 4.</strong> Проводник длиной 20 м и площадью поперечного сечения 0,5 мм² имеет сопротивление 1,12 Ом. Определите, из какого материала изготовлен проводник (используя табличные значения удельных сопротивлений).</p><p><strong>Дано:</strong></p><p>$l = 20$ м</p><p>$S = 0,5$ мм²</p><p>$R = 1,12$ Ом</p><p>Перевод в СИ:</p><p>$S = 0,5 \text{ мм}^2 = 0,5 \cdot 10^{-6} \text{ м}^2$</p><p><strong>Найти:</strong></p><p>Материал проводника ($\rho$ - ?)</p><p><strong>Решение:</strong></p><p>Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим удельное сопротивление $\rho$:</p><p>$\rho = \frac{R \cdot S}{l}$</p><p>Подставим значения в системе СИ:</p><p>$\rho = \frac{1,12 \text{ Ом} \cdot 0,5 \cdot 10^{-6} \text{ м}^2}{20 \text{ м}} = \frac{0,56}{20} \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 0,028 \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$</p><p>Сравнив полученное значение с табличными данными ($ \rho_{алюминий} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м} $), делаем вывод, что проводник изготовлен из алюминия.</p><p><strong>Ответ:</strong> Проводник 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[] #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 {#1187 #items: array:1 [ 0 => App\Models\Term {#1188 #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" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1190 #items: array:1 [ 0 => App\Models\Term {#1191 #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" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #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 {#1192 #items: array:1 [ 0 => App\Models\Term {#1193 #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 [ …6] "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 [ …6] "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 {#1194 #items: array:1 [ 0 => App\Models\Term {#1195 #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 [ …6] "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 [ …6] "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 {#1196 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1197 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1198 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Term {#1200 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1202 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" "alt" => "" "width" => "1608" "height" => "2576" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1204 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1205 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1207 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 4168 "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 {#1181} "field_class" => Illuminate\Database\Eloquent\Collection {#1183} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1185} "field_author" => Illuminate\Database\Eloquent\Collection {#1187} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1189} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1190} "field_country" => Illuminate\Database\Eloquent\Collection {#1192} "field_city" => Illuminate\Database\Eloquent\Collection {#1194} "field_series" => Illuminate\Database\Eloquent\Collection {#1196} "field_umk" => Illuminate\Database\Eloquent\Collection {#1197} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1198} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1199} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1201} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1202} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" "alt" => "" "width" => "1608" "height" => "2576" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1203} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1204} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1205} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1206} "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 {#1536 #items: array:1 [ 0 => App\Models\BookPage {#1212 #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" => 1492013 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "121" "field_url" => "/8-klass/fizika/izergin-uchebnik/page-121" "field_display_title" => "121" "field_folder" => "1" "field_image_name" => "121" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1215 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Book {#1216 #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" => 4168 "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 {#1217 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1223 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1225 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1226 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1228 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1230 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1232 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1233 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1234 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1235 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1237 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1238 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1239 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1240 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1241 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1242 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4168 "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 {#1217 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1223 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1225 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1226 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1228 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1230 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1232 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1233 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1234 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1235 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1237 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1238 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1239 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1240 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1241 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1242 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1244 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ 0 => App\Models\Element {#1246 #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" => 1774914 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1247 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1774914 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1247 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1492014" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1492012" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:2 [ 0 => App\Models\Task {#1255 #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" => 1492413 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "120" "field_page_end" => "121" "field_url" => "/8-klass/fizika/izergin-uchebnik/19-15" "field_display_title" => "15" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 …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 {#1258 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 …2} "content" => Illuminate\Database\Eloquent\Collection {#1332 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1349 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492413 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "120" "field_page_end" => "121" "field_url" => "/8-klass/fizika/izergin-uchebnik/19-15" "field_display_title" => "15" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256 …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 {#1258 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1259 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 …2} "content" => Illuminate\Database\Eloquent\Collection {#1332 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1349 …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 => "*" ] } 1 => App\Models\Task {#1350 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] 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№16 (с. 121)
Условие. №16 (с. 121)
скриншот условия
16*. Используя таблицу 15, составьте несколько различных задач на расчёт электрического сопротивления проводника.
Решение. №16 (с. 121)
Поскольку таблица 15 не предоставлена, для составления и решения задач будут использоваться стандартные значения удельных электрических сопротивлений некоторых распространенных материалов (при температуре 20 °C), которые будут приводиться в условии каждой задачи.
Ниже представлены несколько различных задач на расчет электрического сопротивления проводника.
Задача 1. Рассчитайте сопротивление медного провода длиной 100 м и площадью поперечного сечения 2 мм².
Дано:
$l = 100$ м
$S = 2$ мм²
Удельное сопротивление меди, $\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$
Перевод в СИ:
$S = 2 \text{ мм}^2 = 2 \cdot 10^{-6} \text{ м}^2$
$\rho_{м} = 0,017 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$
Найти:
$\text{R}$ - ?
Решение:
Формула для расчета сопротивления проводника:
$R = \rho \frac{l}{S}$
Подставим значения в системе СИ:
$R = 1,7 \cdot 10^{-8} \text{ Ом} \cdot \text{м} \cdot \frac{100 \text{ м}}{2 \cdot 10^{-6} \text{ м}^2} = \frac{1,7 \cdot 100}{2} \cdot 10^{-8 - (-6)} \text{ Ом} = 85 \cdot 10^{-2} \text{ Ом} = 0,85 \text{ Ом}$
Ответ: 0,85 Ом.
Задача 2. Алюминиевый провод имеет сопротивление 5 Ом и площадь поперечного сечения 1 мм². Какова длина этого провода?
Дано:
$R = 5$ Ом
$S = 1$ мм²
Удельное сопротивление алюминия, $\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$
Перевод в СИ:
$S = 1 \text{ мм}^2 = 1 \cdot 10^{-6} \text{ м}^2$
$\rho_{а} = 0,028 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$
Найти:
$\text{l}$ - ?
Решение:
Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим длину проводника $\text{l}$:
$l = \frac{R \cdot S}{\rho}$
Подставим значения в системе СИ:
$l = \frac{5 \text{ Ом} \cdot 1 \cdot 10^{-6} \text{ м}^2}{2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}} = \frac{5}{2,8} \cdot 10^{-6 - (-8)} \text{ м} \approx 1,786 \cdot 10^2 \text{ м} \approx 178,6 \text{ м}$
Ответ: ≈178,6 м.
Задача 3. Нагревательный элемент изготовлен из нихромовой проволоки длиной 5,5 м. Его сопротивление составляет 22 Ом. Определите площадь поперечного сечения и диаметр проволоки.
Дано:
$l = 5,5$ м
$R = 22$ Ом
Удельное сопротивление нихрома, $\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}}$
Перевод в СИ:
$\rho_{н} = 1,1 \frac{\text{Ом} \cdot \text{мм}^2}{\text{м}} = 1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м}$
Найти:
$\text{S}$ - ?, $\text{d}$ - ?
Решение:
Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим площадь поперечного сечения $\text{S}$:
$S = \frac{\rho \cdot l}{R}$
Подставим значения в системе СИ:
$S = \frac{1,1 \cdot 10^{-6} \text{ Ом} \cdot \text{м} \cdot 5,5 \text{ м}}{22 \text{ Ом}} = \frac{6,05}{22} \cdot 10^{-6} \text{ м}^2 = 0,275 \cdot 10^{-6} \text{ м}^2$
Для наглядности переведем площадь в квадратные миллиметры: $S = 0,275 \text{ мм}^2$.
Площадь поперечного сечения круглого провода связана с его диаметром $\text{d}$ формулой $S = \frac{\pi d^2}{4}$. Выразим диаметр:
$d = \sqrt{\frac{4S}{\pi}}$
Подставим значение площади $\text{S}$ в системе СИ:
$d = \sqrt{\frac{4 \cdot 0,275 \cdot 10^{-6} \text{ м}^2}{\pi}} \approx \sqrt{\frac{1,1 \cdot 10^{-6}}{3,14}} \text{ м} \approx \sqrt{0,35 \cdot 10^{-6}} \text{ м} \approx 0,59 \cdot 10^{-3} \text{ м}$
Переведем диаметр в миллиметры: $d \approx 0,59$ мм.
Ответ: Площадь поперечного сечения $S = 0,275$ мм², диаметр $d \approx 0,59$ мм.
Задача 4. Проводник длиной 20 м и площадью поперечного сечения 0,5 мм² имеет сопротивление 1,12 Ом. Определите, из какого материала изготовлен проводник (используя табличные значения удельных сопротивлений).
Дано:
$l = 20$ м
$S = 0,5$ мм²
$R = 1,12$ Ом
Перевод в СИ:
$S = 0,5 \text{ мм}^2 = 0,5 \cdot 10^{-6} \text{ м}^2$
Найти:
Материал проводника ($\rho$ - ?)
Решение:
Из формулы сопротивления $R = \rho \frac{l}{S}$ выразим удельное сопротивление $\rho$:
$\rho = \frac{R \cdot S}{l}$
Подставим значения в системе СИ:
$\rho = \frac{1,12 \text{ Ом} \cdot 0,5 \cdot 10^{-6} \text{ м}^2}{20 \text{ м}} = \frac{0,56}{20} \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 0,028 \cdot 10^{-6} \text{ Ом} \cdot \text{м} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м}$
Сравнив полученное значение с табличными данными ($ \rho_{алюминий} = 2,8 \cdot 10^{-8} \text{ Ом} \cdot \text{м} $), делаем вывод, что проводник изготовлен из алюминия.
Ответ: Проводник изготовлен из алюминия.
Другие задания:
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