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Консультация № 171844
03.09.2009, 01:03
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Уважаемые эксперты, прошу помочь.
Обмотка соленоида имеет сопротивление 10 Ом. Какова его индуктивность, если при прохождение тока за 0,05 с в нем веделяется количество теплоты, эквивалентное энергии магнитного поля соленоида?
Спасибо за помощь.
Обмотка соленоида имеет сопротивление 10 Ом. Какова его индуктивность, если при прохождение тока за 0,05 с в нем веделяется количество теплоты, эквивалентное энергии магнитного поля соленоида?
Спасибо за помощь.
Обсуждение
03.09.2009, 10:15
общий
это ответ
Здравствуйте, Шаврин Андрей Сергеевич.
Обозначим: L - искомая индуктивность соленоида, W - энергия магнитного поля соленоида, Q - количество теплоты, выделяемое в обмотке соленоида за время T = 0.05 с, R = 10 Ом - сопротивление обмотки соленоида, I - конечное значение тока в обмотке соленоида. Тогда W = L*I2/2 (1). Если принять, по умолчанию, что ток в обмотке соленоида за всё время T не меняется и равен I, то Q = I2*R*T (2) - закон Джоуля-Ленца. В этом случае, приравняв (1) и (2), получаем: L = 2*R*T = 2*10*0.05 = 1 Гн. Если же, к примеру, ток равномерно возрастает от 0 до I, то, путём интегрирования, получается Q = I[sup]2[/sup]*R*T/3, и в этом случае L = 1/3 Гн.
Обозначим: L - искомая индуктивность соленоида, W - энергия магнитного поля соленоида, Q - количество теплоты, выделяемое в обмотке соленоида за время T = 0.05 с, R = 10 Ом - сопротивление обмотки соленоида, I - конечное значение тока в обмотке соленоида. Тогда W = L*I2/2 (1). Если принять, по умолчанию, что ток в обмотке соленоида за всё время T не меняется и равен I, то Q = I2*R*T (2) - закон Джоуля-Ленца. В этом случае, приравняв (1) и (2), получаем: L = 2*R*T = 2*10*0.05 = 1 Гн. Если же, к примеру, ток равномерно возрастает от 0 до I, то, путём интегрирования, получается Q = I[sup]2[/sup]*R*T/3, и в этом случае L = 1/3 Гн.
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