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Консультация № 132879
18.04.2008, 20:25
0.00 руб.
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380. Источник тока замкнули на катушку сопротивлением R=20 Ом. Через время t=0,1с тока I в катушке достигла 0,95 предельного значения. Определить индуктивность L катушки.
Обсуждение
19.04.2008, 07:32
общий
это ответ
Здравствуйте, Курбан!
Во время переходного процесса в цепи с индуктивностью и сопротивлением процесс изменения текущего значения тока I во времени описывается уравнением: I = I<sub>m</sub>(1 - e<sup>-(R/L)*t</sup>) (1), где I<sub>m</sub> - предельное значение тока, e - основание натуральных логарифмов; (см. http://fishelp.ru/toe1/perechodn.html "Подключение R-L цепи к источнику постоянной ЭДС"). Если обозначить: I<sub>д0.1</sub> = 0.95*I<sub>m</sub> (2) - достигнутое через t = t<sub>0.1</sub> = 0.1 (3) с значение тока I, уравнение (1) можно переписать: I<sub>д0.1</sub> = I<sub>m</sub>(1 - e<sup>-(R/L)*t<sub>0.1</sub></sup>) (4), откуда e<sup>-(R/L)*t<sub>0.1</sub></sup> = 1 - I<sub>д0.1</sub>/I<sub>m</sub> (5), или, поскольку e<sup>-(R/L)*t<sub>0.1</sub></sup> = 1/e<sup>(R/L)*t<sub>0.1</sub></sup>: e<sup>(R/L)*t<sub>0.1</sub></sup> = 1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>) (6). Далее, логарифмируя обе части (6): (R/L)*t<sub>0.1</sub> = LN(1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>)) (7), откуда L = R*t<sub>0.1</sub>/LN(1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>)), или, подставляя числа: L = 20*0.1/LN(1/(1 - 0.95)) = 2/LN(20) = 0.67 Гн.
Во время переходного процесса в цепи с индуктивностью и сопротивлением процесс изменения текущего значения тока I во времени описывается уравнением: I = I<sub>m</sub>(1 - e<sup>-(R/L)*t</sup>) (1), где I<sub>m</sub> - предельное значение тока, e - основание натуральных логарифмов; (см. http://fishelp.ru/toe1/perechodn.html "Подключение R-L цепи к источнику постоянной ЭДС"). Если обозначить: I<sub>д0.1</sub> = 0.95*I<sub>m</sub> (2) - достигнутое через t = t<sub>0.1</sub> = 0.1 (3) с значение тока I, уравнение (1) можно переписать: I<sub>д0.1</sub> = I<sub>m</sub>(1 - e<sup>-(R/L)*t<sub>0.1</sub></sup>) (4), откуда e<sup>-(R/L)*t<sub>0.1</sub></sup> = 1 - I<sub>д0.1</sub>/I<sub>m</sub> (5), или, поскольку e<sup>-(R/L)*t<sub>0.1</sub></sup> = 1/e<sup>(R/L)*t<sub>0.1</sub></sup>: e<sup>(R/L)*t<sub>0.1</sub></sup> = 1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>) (6). Далее, логарифмируя обе части (6): (R/L)*t<sub>0.1</sub> = LN(1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>)) (7), откуда L = R*t<sub>0.1</sub>/LN(1/(1 - I<sub>д0.1</sub>/I<sub>m</sub>)), или, подставляя числа: L = 20*0.1/LN(1/(1 - 0.95)) = 2/LN(20) = 0.67 Гн.
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