Question

In the circuit shown below, the ac source has voltage v = 20 cos ωt volts with ω = 2000 rad/ sec. The amplitude of the current will be nearest to

(a) 2 A 

(b) 3.3 A 

(c) 21√5 A 

(d) 5 A

Answer 1

The correct option (a) 2A

Explanation:

Given  ω = 2000 rad/sec

L = 5 mH

C = 50 μF

R = 6Ω + 4Ω = 10Ω

X_L = ωL = 2000 × 5 × 10^–3 = 10Ω

X_C = (1/ωL) = [1/{2000 × 50 × 10^–6}] = (1/0.1) = 10Ω

as X_L = X_C hence resonance occurs & current in the circuit is

I_max = [{V_max}/{R}]

∴ I_max = (20/10) = 2A.