An emf E = 4 cos (1000t) volt is applied to an LR circuit of inductance 3 mH and resistance 4 `Omega`. What is the amplitude of current in the circuit ?

Options

A. `4/sqrt7A`
B. 1.0 A
C. `4/7`A
D. 0.8 A

Answer

C

Explanation

`X_L=omegaL=10^3xx3xx10^3=3Omega`
`|Z|=sqrt(R^2+X_L^2)`
`=sqrt((4)^2+(3)^2)`
`=sqrt25`
`|Z|=5Omega` and `E_m`=4V
`therefore E_"rms"=E_m/sqrt2=4/1.414`=2.828 V
`therefore I_"rms"=E_"rms"/"|Z|"`
`=2.828/5`
=0.567
`approx` 0.57
`approx 4/7A`