A current of 4 A flows in a coil when connected to a 12 V dc source. If the same coil is connected to a `12 V, 50 rad s^(-1)` ac source, a current of 2.4 A flows of the coil in the circuit.
The inductance of the coil is

Options

A. 0.08H
B. 0.04 H
C. 0.02 H
D. 1 H

Answer

A

Explanation

A coil consists of an inductance (L) and a resistance (R). In dc only resistance is effective. Hence,
`R = (V)/(i) = (12)/(4) = 3Omega`
In ac, `i_(rms) = (V_(rms))/(Z) = (V_(rms))/(sqrt(R^(2) + omega^(2)L^(2)))`
`Rightarrow L = (1)/(omega) sqrt(((V_(rms))/(i_(rms))) - R^(2)) = (1)/50sqrt(((12)/(2.4))^(2) - (3)^(2))`
= 0.08 henry