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NCERT Class XII Chapter
Alternating Current
Questions With Solutions

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Question : 21
Total: 26
Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H, C = 27 μF, and R = 7.4 Ω. It is desired to improve the sharpness of the resonance of the circuit by reducing its ‘full width at half maximum’ by a factor of 2. Suggest a suitable way.
Solution:  
vr =
1
2π√LC
 =
1
2×3.14×√3×27×10−6
 =
1000
6.28×9
 = 17.7
resonant frequency, ωr = 2πvr = 2 × 3.14 × 17.7 = 111 rad sec–1
Quality factor in the given resonant circuit
Q =
1
₹
√
L
C
 =
1
7.4
√
3
27×10−6
 = 45
we want to improve the quality factor to twice, without changing resonant frequency (without changing L and C).
Q' = 2Q = 90 =
1
R′
√
L
C
or R' =
1
90
√
3
27×10−6
 = 3.7 Ω
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