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Консультация № 179650
02.08.2010, 14:16
0.00 руб.
0
6
1
Здравствуйте,
На рисунке сопротивление каждого проводника, включенного между двумя узлами, равно 1 Ом. Найти сопротивление цепи.
http://s55.radikal.ru/i148/1008/c9/b163d4d33aac.jpg
На рисунке сопротивление каждого проводника, включенного между двумя узлами, равно 1 Ом. Найти сопротивление цепи.
http://s55.radikal.ru/i148/1008/c9/b163d4d33aac.jpg
Обсуждение
02.08.2010, 15:50
общий
это ответ
Здравствуйте, ataman.
Дважды выполним преобразование звезда-треугольник, сначала для проводников, помеченных красным, потом -- синим. (Формулы приведены здесь.) То, то получается в результате преобразования, показано на втором рисунке. Замечаем, что по средней паре (вертикальных) проводников ток идти не может из-за симметрии цепи. Следовательно, эти два проводника можно исключить. Сопротивление R цепи равно половине сопротивления нижней и верхней ветвей:
R= (1+3/2)/2 = 5/4 Ом.
Дважды выполним преобразование звезда-треугольник, сначала для проводников, помеченных красным, потом -- синим. (Формулы приведены здесь.) То, то получается в результате преобразования, показано на втором рисунке. Замечаем, что по средней паре (вертикальных) проводников ток идти не может из-за симметрии цепи. Следовательно, эти два проводника можно исключить. Сопротивление R цепи равно половине сопротивления нижней и верхней ветвей:
R= (1+3/2)/2 = 5/4 Ом.
5
02.08.2010, 18:10
общий
Можно проще: потенциалы точек 2 и 6 равны (симметрия), поэтому их можно безболезненно соединить. По этой же причине можно соединить 3 и 5. Ну а дальше - совсем просто.
Неизвестный
03.08.2010, 13:28
общий
Lang21:
Здравствуйте
"Формулы приведены здесь".При открытии вышеуказанной ссылки возникла проблема-"В Википедии нет статьи с таким названием".Будьте любезны перезалейте ссылочку или отправьте те самые формулы в мини-форум, спасибо
Здравствуйте
"Формулы приведены здесь".При открытии вышеуказанной ссылки возникла проблема-"В Википедии нет статьи с таким названием".Будьте любезны перезалейте ссылочку или отправьте те самые формулы в мини-форум, спасибо
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