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Q.

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

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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

answer is A.

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Detailed Solution

For dc,  R=Vi=1001=100  ΩFor ac,  Z=Vi=1000.5=200  Ω∵   Z=R2+(ωL)2⇒200=(100)2+4π2(50)2L2∴L=0.55  H
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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