Question

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]

• A. 4.98
• B. 5.58
• C. 6.32
• D. 6.90

Answer 1

Answer: (C)

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 $=Q=\frac{1}{2}\sqrt{\frac{L}{10}}=\frac{1}{10}\sqrt{\frac{200\times {10}^{-3}}{50\times {10}^{-6}}}=6.32$