Question

In an $LR$ circuit, the value of $L$ is $ \bigg( \frac{ 0.4}{ \pi}\bigg) $ $H$ and the value of $R$ is $30\,\Omega$ . If in the circuit, an alternating emf of $200\, V$ at $50 \,cycle/s$ is connected, the impedances of the circuit and current will be

• A. 11.40 $\Omega$ , 17.5 A
• B. 30.7 $\Omega$ , 6.5 A
• C. 40.4 $\Omega$, 5 A
• D. 50, $\Omega$ 4 A

Answer 1

Answer: (D)

Given, $ X_L = \omega L= 2 \pi fL$
= $ 2 \pi \times 50 = \frac{ 0.4}{ \pi}$
= 40 $\Omega$
R = 30$\Omega$
Z = $ \sqrt{ R^2 + X_L^2}$
= $ \sqrt{ (30)^2 + (40)^2 } = 50 \,\Omega$
$ i_{rms} = \frac{ V_{ rms}}{ Z}$
= $ \frac{ 200}{ 50} = 4 $ A