An ideal inductive coil has a resistance of `100gamma` When an ac signal of frequency `100Hz` is applied to the coil the voltage leads the current by `45^(@)` The inductance of the coil is .

Options

A. `(1)/(10pi)H`
B. `(1)/(20pi)H`
C. `(1)/(40pi)H`
D. `(1)/(60pi)H`

Answer

B

Explanation

`tan phi = X_(L)/ R implies tan 45^(@) = X_(L)/(100) implies X_(L) =100 Omega`
`X_(L) = omegaL =2 pi fL =100`
`2pi xx 1000 L = 100`
`L = (1)/(20pi) H` .