An e.m.f. `E=4cos(1000t)`volt is applied to an `LR` circuit of inductance `3mH` and resistance `4ohm`. The amplitude of current in the circuit is

Options

A. 1.0A
B. `4/7 A`
C. `0.8 A`
D. `4/(sqrt(7))A`

Answer

C

Explanation

` E = 4 cos (1000t)`
`:. E_(0) = 4 V and omega = 1000`
`:.` inductive reactance `X_(L) = omega L = 1000 xx 3 xx 10^(-3) = 3 Omega`
`:.` Impedance `Z = sqrt(R^(2)+X_(L)^(2)) = sqrt(4^(2)+3^(2))=5`
`I_(0) = (V_0)/(Z) = 4/5 = 0.8 A`.