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Консультация № 180066
28.09.2010, 00:58
40.68 руб.
0
2
2
Здраствуйте, эксперты!))) Помогите решить задачу!))) 
*
Источник тока замкнули на катушку сопротивлением R=10 Ом и индуктивностью L=0,2Гн. Через какое время сила тока в цепи достигнет 50% максимального значения?
*
Источник тока замкнули на катушку сопротивлением R=10 Ом и индуктивностью L=0,2Гн. Через какое время сила тока в цепи достигнет 50% максимального значения?
Обсуждение
28.09.2010, 01:17
общий
это ответ
Здравствуйте, Real Madrid Player.
Дано: R = 10 Ом, I = 0.5*I0, L=0,2 Гн
Решение:
Мгновенное значение силы тока в цепи, обладающей сопротивлением R и индуктивностью L при замыкании цепи равно
I=I0*(1-e-R*t/L)
Поэтому (R*t)/L=-ln(1-I/I0) , откуда искомая величина
t=-L/R*ln(1-I/I0)
Подставляем числа:
t=-0,2/10*ln(1-0,5)=-0,02*(-0,69)=0,0138 с =13,8 мс
Ответ:t=13,8 мс
Дано: R = 10 Ом, I = 0.5*I0, L=0,2 Гн
Решение:
Мгновенное значение силы тока в цепи, обладающей сопротивлением R и индуктивностью L при замыкании цепи равно
I=I0*(1-e-R*t/L)
Поэтому (R*t)/L=-ln(1-I/I0) , откуда искомая величина
t=-L/R*ln(1-I/I0)
Подставляем числа:
t=-0,2/10*ln(1-0,5)=-0,02*(-0,69)=0,0138 с =13,8 мс
Ответ:t=13,8 мс
Неизвестный
28.09.2010, 19:16
общий
это ответ
Здравствуйте, Real Madrid Player!
Во время переходного процесса в цепи с индуктивностью и сопротивлением процесс изменения текущего значения тока I во времени описывается уравнением:
I = Im(1 - e^(-(R/L)*t)) (1) , где Im - предельное значение тока, e - основание натуральных логарифмов; Уравнение (1) можно переписать: I/Im = 1 - e^(-(R/L)*t) (2), откуда e^(-(R/L)*t) = 1 - I/Im (3). Логарифмируя обе части (3): (R/L)*t = LN(1/(1 - I/Im)) (4), откуда t = (L/R)*LN(1/(1 - I/Im)), или, подставляя числа: t = (0.2/10)*LN(1/(1 - 0.5) = 0.02*LN(2) = 0.01386 с.
Приложение:
Для дополнительной информации:
http://fishelp.ru/toe1/perechodn.html "Подключение R-L цепи к источнику постоянной ЭДС"
Во время переходного процесса в цепи с индуктивностью и сопротивлением процесс изменения текущего значения тока I во времени описывается уравнением:
I = Im(1 - e^(-(R/L)*t)) (1) , где Im - предельное значение тока, e - основание натуральных логарифмов; Уравнение (1) можно переписать: I/Im = 1 - e^(-(R/L)*t) (2), откуда e^(-(R/L)*t) = 1 - I/Im (3). Логарифмируя обе части (3): (R/L)*t = LN(1/(1 - I/Im)) (4), откуда t = (L/R)*LN(1/(1 - I/Im)), или, подставляя числа: t = (0.2/10)*LN(1/(1 - 0.5) = 0.02*LN(2) = 0.01386 с.
Приложение:
Для дополнительной информации:
http://fishelp.ru/toe1/perechodn.html "Подключение R-L цепи к источнику постоянной ЭДС"
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