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Question: The self inductance of a choke coil is 10 mH. When it is connected with a 10V dc source, then the lo...

The self inductance of a choke coil is 10 mH. When it is connected with a 10V dc source, then the loss of power is 20 watt. When it is connected with 10 volt ac source loss of power is 10 watt. The frequency of ac source will be

A

50 Hz

B

60 Hz

C

80 Hz

D

100 Hz

Answer

80 Hz

Explanation

Solution

With dc : P=V2RP = \frac { V ^ { 2 } } { R } Ž R=(10)220=5ΩR = \frac { ( 10 ) ^ { 2 } } { 20 } = 5 \Omega;

With ac : P=Vrms2RZ2P = \frac { V _ { r m s } ^ { 2 } R } { Z ^ { 2 } }

Ž Z2=(10)2×510=50Ω2Z ^ { 2 } = \frac { ( 10 ) ^ { 2 } \times 5 } { 10 } = 50 \Omega ^ { 2 }

Also Z2=R2+4π2v2L2Z ^ { 2 } = R ^ { 2 } + 4 \pi ^ { 2 } v ^ { 2 } L ^ { 2 }

Ž 50=(5)2+4(3.14)2v2(10×10−3)250 = ( 5 ) ^ { 2 } + 4 ( 3.14 ) ^ { 2 } v ^ { 2 } \left( 10 \times 10 ^ { - 3 } \right) ^ { 2 }

Ž