If the power factor of series L-C-R circuit is unity, then Q-factor is [take, v = 50 Hz]
A) 4.98
B) 5.58
C) 6.32
D) 6.90
Correct Answer: C
Solution :
As the power factor for series L-C-R circuit is unity. It shows the circuit is resonating one with resonance frequency \[v=\frac{1}{2\pi \sqrt{LC}}\Rightarrow C=\frac{1}{4{{\pi }^{2}}{{v}^{2}}L}\] \[=\frac{1}{4{{\pi }^{2}}\times {{(50)}^{2}}\times 200\times {{10}^{-3}}}\simeq 50\mu F\] Now, Q-factor \[=Q=\frac{1}{2}\sqrt{\frac{L}{10}}=\frac{1}{10}\sqrt{\frac{200\times {{10}^{-3}}}{50\times {{10}^{-6}}}}=6.32\]
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