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Question

In a series LCR circuit having L = 30 mH, R = 8 Ω and the resonant frequency is 50 Hz. The quality factor of the circuit is:

A
0.118
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B
11.8
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C
118
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D
1.18
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Solution

The correct option is D 1.18
L=30MH
R=8Ω
resonant freq =50Hz
ω=2πf=100π
Quantity factor =Q=1RLC

=1RLC(1)
At resonance condition.
(100π)2=130×103C

C=130×103×(100π)2
Now in (1) -
Q=1830×103×30×103×(100π)21
=18900×106×104π2

=18×30×101×π

=3π8
=1.1775

1.18.

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