Question

In a L-R circuit, the value of L is $\left( \frac{0.4}{\pi} \right)\mspace{6mu} henry$ and the value of R is 30 ohm. If in the circuit, an alternating e.m.f. of 200 volt at 50 cycles per sec is connected, the impedance of the circuit and current will be

• A. $11.4\Omega,17.5A$
• B. $30.7\Omega,6.5A$
• C. $40.4\Omega,5A$
• D. $50\Omega,4A$

Answer 1

Answer: (D)

$50\Omega,4A$

Answer 2

$Z = \sqrt{R^{2} + X^{2}} = \sqrt{R^{2} + (2\pi fL)^{2}}$

=$\sqrt{(30)^{2} + \left( 2\pi \times 50 \times \frac{0.4}{\pi} \right)^{2}} = \sqrt{900 + 1600} = 50\Omega$

$i = \frac{V}{Z} = \frac{200}{50} = 4ampere$