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  4. Consider the circuit shown below If the power factor of series L-C-R circuit is unity, then Q-factor is [take, v = 50 Hz]

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Q. Consider the circuit shown below
If the power factor of series L-C-R circuit is unity, then Q-factor is [take, v = 50 Hz]Physics Question Image

CMC MedicalCMC Medical 2015

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 $