An e.m.f. `E = 200 sin 377 `t volt is applied across an inductance L having a resistance of 1.0 ohm. The maximum current is found to be 10 A. Find the value of L.

Explanation

Here, `E = 200 sin 377 t , R = 1.0 ohm`,
`I_(0) = 10 A. L = ? :. E_(0) = 200 V, omega = 377`
`Z = (E_(0))/(I_(0)) = (200)/(10) = 20 ohm`
As `Z^(2) = R^(2) + X_(L)^(2)`
`:. X_(L) = sqrt(Z^(2) - R^(2)) = sqrt(20^(2) - 1^(2)) = 20`
Now, `X_(L) = omega L = 20`,
`L = (20)/(omega) = (20)/(377) = 0.053 H = 53 mH`