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Консультация № 182280
21.02.2011, 18:46
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Колебательный контур состоит из катушки индуктивностью L = 0,1 Гн и конденсатора емкостью C = 40 мкФ. Максимальный заряд конденсатора Qm = 3 мкКл. Пренебрегая сопротивлением контура, записать уравнения изменения силы тока в цепи и изме-нения напряжения на конденсаторе в зависимости от времени.
Если не сложно, то просьба с подробным решением.
Заранее благодарен.
Колебательный контур состоит из катушки индуктивностью L = 0,1 Гн и конденсатора емкостью C = 40 мкФ. Максимальный заряд конденсатора Qm = 3 мкКл. Пренебрегая сопротивлением контура, записать уравнения изменения силы тока в цепи и изме-нения напряжения на конденсаторе в зависимости от времени.
Если не сложно, то просьба с подробным решением.
Заранее благодарен.
Обсуждение
21.02.2011, 19:47
общий
22.02.2011, 05:41
это ответ
Здравствуйте, Сергей!
Если пренебречь сопротивлением контура (R=0), имеем свободные гармонические колебания, описываемые уравнениями q = q[sub]0[/sub] sin(ωt + φ[sub]0[/sub]) и I = I[sub]0[/sub] cos(ω t + φ[sub]0[/sub]), где q, I - заряд конденсатора и сила тока, q[sub]0[/sub], I[sub]0[/sub] - их амплитуды, φ[sub]0[/sub] - начальная фаза, ω - циклическая частота, равная
В данном случае
и q[sub]0[/sub] = 0.000003 Кл. Принимая φ[sub]0[/sub] = 0, имеем
Амплитуда силы тока равна I[sub]0[/sub] = ωq[sub]0[/sub] = 500*0.000003 = 0.0015 А, поэтому сила тока описывается уравнением
Напряжение на конденсаторе совпадает по фазе с зарядом и определяется формулой U = q/C = U[sub]0[/sub] sin(ω t + φ[sub]0[/sub]), где U[sub]0[/sub] = q[sub]0[/sub]/C - амплитуда напряжения. В данном случае U[sub]0[/sub] = 0.000003/0.00004 = 0.075 В и напряжение описывается уравнением
Если пренебречь сопротивлением контура (R=0), имеем свободные гармонические колебания, описываемые уравнениями q = q[sub]0[/sub] sin(ωt + φ[sub]0[/sub]) и I = I[sub]0[/sub] cos(ω t + φ[sub]0[/sub]), где q, I - заряд конденсатора и сила тока, q[sub]0[/sub], I[sub]0[/sub] - их амплитуды, φ[sub]0[/sub] - начальная фаза, ω - циклическая частота, равная
В данном случае
и q[sub]0[/sub] = 0.000003 Кл. Принимая φ[sub]0[/sub] = 0, имеем
Амплитуда силы тока равна I[sub]0[/sub] = ωq[sub]0[/sub] = 500*0.000003 = 0.0015 А, поэтому сила тока описывается уравнением
Напряжение на конденсаторе совпадает по фазе с зарядом и определяется формулой U = q/C = U[sub]0[/sub] sin(ω t + φ[sub]0[/sub]), где U[sub]0[/sub] = q[sub]0[/sub]/C - амплитуда напряжения. В данном случае U[sub]0[/sub] = 0.000003/0.00004 = 0.075 В и напряжение описывается уравнением
5
Благодарю!!
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