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Задать вопрос экспертам

Консультация № 200746

27.04.2021, 16:38

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0 1 1

Образование

Здравствуйте! Прошу помощи в следующем вопросе:
Колебательный контур состоит из катушки индуктивностью L=100 мГн и
конденсатора емкостью С=100 пФ. Сколько времени проходит от момента,
когда конденсатора полностью разряжен, до момента, когда его энергия
вдвое превышает энергию катушки? Активным сопротивлением катушки
пренебречь.

Обсуждение

давно

Посетитель
226425
1567

28.04.2021, 23:00

общий

это ответ

Дано:
L=0,1 Гн
C=10^-10Ф
q_o=0 [$8658$] i_o=I_max
W_C1=2W_L1
Найти: t₁
Решение:
1. Энергия электрического поля конденсатора
W_C=q₂/2C = (1/2C)*(q_max*sin[$969$]t)² (1)
2. Энергия магнитного поля катушки
W_L=Li²/2
i=q`(t) = [$969$]*q_max*cos[$969$][$969$]t
Следовательно
W_L=(1/2)*L*([$969$]*q_max*cos[$969$]t)² (2)
3. По условию
W_C1/W_L1 = 2
Следовательно, после подстановки (1) и (2), возведения в квадрат множителей в скобках и сокращения получаем
2= sin²([$969$]*t₁)/[LC*cos²([$969$]*t₁)]
[$8658$]
2LC=tg²([$969$]*t₁)
[$8658$]
tg²([$969$]*t₁)=20*10^-12
tg([$969$]*t₁)=4,47*10^-6
[$966$]₁=[$969$]*t₁=4,47*10^-6
[$969$]=1/[$8730$](LC)
[$8658$]
t₁=[$966$]₁/[$969$]=[$966$]₁*[$8730$](LC)=4,47*10^-6*[$8730$](10^-11)[$8776$]14*10^-6c
t₁=14 мкс
*******
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Об авторе:
С уважением
shvetski

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