Question

A sinusoidaI voltage of peak value 300 V and an angular frequency $\omega$ = 400 rad/s is applied to series L-C-R circuit, in which R = 3 $\Omega$, L = 20 mH and C = 625 $\mu$F. The peak current in the circuit is

• A. 30 $ \sqrt 2$ A
• B. 60 A
• C. 100 A
• D. 60 $ \sqrt 2 $A

Answer 1

Answer: (B)

The impedance of the circuit is
Z = $ \sqrt{ R^2 + ( X_L - X_C)^2 } $
$ X_L = \omega L = 400 \times 20 \times 10^{ - 3} = 8$ H
$ X_C = \frac{ 1}{ \omega C} = \frac{ 1}{ 400 \times 625 \times 10^{ - 6}} = 4 F $
Z = $ \sqrt{ ( 3)^2 + ( 8 - 4 )^2 } = 5 $
i = $ \frac{ E}{ Z} = \frac{ 300}{ 5 } = 60$ A