The resistance of an R-L A.C. circuit is 10 `Omega`. An emf `E_0` applied across the circuit at `omega=20` rad/s . If the current in the circuit is `I_0/sqrt2` what is the value of L ?

Options

A. 0.55 H
B. 0.15 H
C. 0.5 H
D. 0.4 H

Answer

C

Explanation

Here `R=10 Omega`
`omega`=20 rad/s
`I=I_0/sqrt2`
`rArr` Impedence of series connection of R-L
`|Z|=sqrt(R^2+(omegaL)^2)`
Current in circuit `I=E_0/"|Z|"`
`I_0/sqrt2=E_0/(R(sqrt(1+((omegaL)/R)^2)))`
`I_0/sqrt2=I_0/sqrt(1+((omegaL)/R)^2)[because E_0/R=I_0]`
`therefore 1/sqrt2=1/sqrt(1+((omegaL)/R)^2)`
`therefore 2=1+((omegaL)/R)^2`
`therefore 1=((omegaL)/R)^2`
`therefore 1=(omegaL)/R`
`therefore L=R/omega`
`therefore L=10/20`
`therefore` L=0.5 H