The phase angle between the current and voltage in an L-R circuit is `30^(@)`. What is the impendance of the circuit if the resistance in the circuit is `10sqrt(3) Omega`?

Options

A. 1 H
B. 2 H
C. 3 H
D. 0.5 H

Answer

D

Explanation

`I (V_(0))/( Z) = (E_(0))/(sqrt(R^(2) + (omega L)^(2)))= (i_(0))/([1 + ((omegaL)/(R))^(2)]^((1)/(2)))`
`rArr (i_(0))/(sqrt(2)) = (i_(0))/([1+ ((omegaL)/(R))^(2)]^((1)/(2)))rArr 1 + ((omega L)/(R))^(2) = 2 `
`rArr (omega L)/( R) = 1 rArr L = (R)/(omega) = (10)/(20) = 0.5 H`