An inductive coil has a resistance of `100 Omega`. When an AC signal of frequency 1000 Hz is applied to the coil, the voltage leads the current by `45^(@)`. What is the inductance of the coil?

Options

A. `6.7 xx10^(-7)` H
B. `5.5 xx10^(-5)`H
C. `1.1 xx10^(-1)` H
D. `1.1 xx10^(-2)` H

Answer

D

Explanation

L-R circuit
tan ` 45^(@) = (x_(1))/R`
` 1 = (x_(1))/E rArr x_(1) = R`
Now `Z= sqrt(R^(2)+x_(1)^(2))`
or `Z = sqrt(x_(1)^(2) +x_(1)^(2) )= sqrt(2x_(1)^(2)) = sqrt(2)x_1`
` 100 = sqrt(2) x_(1)`
` x_(1) = 100/(sqrt(2))`
`omegaL = 100/(sqrt(2)) rArr L = 100/(sqrt(2)omega) = 100 /(sqrt(2) xx2pif) = 100/(sqrt(2)xx2 xx3.14 xx 1000)`
` = 1.1 xx10^(-2)` H