The virtual current of 4 A and 50 Hz flows in an AC circuit contaning a coil. The power consumed in the coil is 240 W. If the virtual voltage across the coil is 100 V, then its resistance will be

Options

A. `(1)/(3 pi)` H
B. `(1)/(5 pi)` H
C. `(1)/(7 pi)` H
D. `(1)/(9 pi)` H

Answer

B

Explanation

Power consumed only by resistance
`R = (P)/(i_(2)) = (240)/( 4 xx 4) = 15 Omega `
`Z = (V)/(i) = (100)/( 4) = 25 Omega `
Now, `Z = sqrt(R^(2) + X_(L)^(2))`
` rArr X_(L) = sqrt(25^(2) - 15 ^(2)) = 20 Omega `
`rarr 2 pi f L = 20 rArr L = (20)/( 2 pi xx 50) = (1 )/( 5 pi ) Hz`