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Question

The bridge shown in figure is used to measure the quality factor of coil. Which is represent by a parallel combination of resistance Rp and inductance Lp, the bridge is balance at 100 Hz, supply frequency.



Choose the correct statement(s).

A
The value of unknown resistance Rp is 8.4kΩ
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B
The value of unknown inductance Lp is 6.3 mH
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C
The quality factor of coil will be 2122.06
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D
Both Rp and Lp are independent of frequency
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Solution

The correct option is D Both Rp and Lp are independent of frequency
Bridge is balanced at 100 Hz.

At balanced condition,

(jωRPLPRP+jωLP)×(R2+1jωC)=R3R4

jωRPLP.R2+RPLPC=R3R4RP+jωLPR3R4

On comparing real and imaginary parts

Rp=R3.R4R2=1.26×5×10575=8.4lΩ

and
Lp=R3.R4.C=1.26×5×105×0.01×106=6.3mH

The quality factor for this bridge circuit can be given by

QP=V2PXLV2PRP=RPωLP=8.4×103200π×6.3×103=2122.06

The coil parameters Rp and Lp, both are independent of frequency.

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