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NCERT Class XII Chapter
Alternating Current
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Question : 6 of 26
Marks: +1, -0
Obtain the resonant frequency ωr of a series LCR circuit with L = 2.0 H, C = 32 µF and R = 10 Ω. What is the Q-value of this circuit?
Solution:  
Resonant angular frequency in series LCR circuit
ωr\omega_r = 1LC\frac{1}{\sqrt{LC}} = 12×32×10−6\frac{1}{\sqrt{2 \times 32 \times 10^{-6}}} = 125 rad/s
Quality factor Q = 1RLC\frac{1}{R} \sqrt{\frac{L}{C}} = 110232×10−6\frac{1}{10} \sqrt{\frac{2}{32 \times 10^{-6}}} = 25
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