First slide

AC Circuits

Question

In a L-R circuit, the value of L is $(\frac{0 .4}{π}) henry$ 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

Moderate

A

$11 .4 Ω, 17 .5 A$
B

$30 .7 Ω, 6 .5 A$
C

$40 .4 Ω, 5 A$
D

$50 Ω, 4 A$

Solution

$Z = \sqrt{R^{2} + X^{2}} = \sqrt{R^{2} + {(2 πfL)}^{2}}$
$\sqrt{{(30)}^{2} + {(2 π \times 50 \times \frac{0 .4}{π})}^{2}} = \sqrt{900 + 1600} = 50 Ω$
$i = \frac{V}{Z} = \frac{200}{50} = 4 ampere$

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