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An inductor (L = 20 mH), a resistor (R =...

An inductor `(L = 20 mH)`, a resistor `(R = 100 Omega)` and a battery`(varepsilon = 10 V) ` are connected in series. Find (a) the time constant, (b) the maximum current and (c ) the time elapsed before the current reaches 99% of the maximum value.

Text Solution

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(a) The time constant is `tau = (L)/(R ) = (20mH)/(100 Omega) = 0
20 ms
(b) The maximum current is ` I = varepsilon /R = (10 V)/(100 Omega) = 0
10 A`
(c ) Using `I = i_0(1-e^(-t/tau), 0
99 i_0 = i_0(1-e^(-t/tau)` or, ` e^(-t/tau) = 0
01)` or, `(t)/(tau) =- In(0
01)` or,`t = (0
20ms) In(100) = 0
92ms.
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