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Question

When 100 volt dc is appiled across a coil, a current of 1 amp flows through it. When 100 V A.C of 50 Hz is appiled to the same coil, only 0.5 amp flows. What is the value of inductance of the coil ?

A
3πH
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B
π3H
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C
2πH
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D
π2H
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Solution

The correct option is A 3πH
When connected to dc source, in steady state, current is constant. So inductor just acts like a conducting wire.
We can draw the circuit as follows



R=100 V1 A=100 Ω

When we connect it to an a.c source, circuit is as follows



Given Vrms=100 V,irms=0.5 A
Vrms=irms×Z
Z=1000.5=200 Ω

Impedance Z for an LR circuit is
Z=R2+X2L
Z2=R2+X2L
2002=1002+X2L

XL=1003=2πfL=2π(50)L
L=3π H

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