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=1.26×5×105×0.01×10−6=6.3mH
⇒ The quality factor for this bridge circuit can be given by