First slide

AC Circuits

Question

When 100 volts dc is supplied across a solenoid, a current of 1.0 amperes flows in it. When 100 volts ac is applied across the same coil, the current drops to 0.5 ampere. If the frequency of ac source is 50 Hz, then the impedance and inductance of the solenoid are

Moderate

A

200 $Ω$ and 0.55 henry
B

100 $Ω$ and 0.86 henry
C

200 $Ω$ and 1.0 henry
D

100 $Ω$ and 0.93 henry

Solution

For dc, $R = \frac{V}{i} = \frac{100}{1} = 100 Ω$
For ac, $Z = \frac{V}{i} = \frac{100}{0 .5} = 200 Ω$
$∵ Z = \sqrt{R^{2} + {(ωL)}^{2}} \Rightarrow 200 = \sqrt{{(100)}^{2} + 4 π^{2} {(50)}^{2} L^{2}}$
$∴ L = 0 .55 H$

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