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Standard XII

Physics

Resonance in RLC Circuit

Figure shows ...

Question

Figure shows a series LCR circuit connected to a variable frequency 230 V source.
The source frequency which drives the circuit in resonance is

4 Hz

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5 Hz

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6 Hz

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8 Hz

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Solution

The correct option is D 8 Hz
Here, $L = 5 H, C = 80 μ F = 80 \times 10^{- 6} F, R = 40 Ω$
$V_{r m s} = 230 V$

The resonant angular frequency is
$ω_{r} = \frac{1}{\sqrt{L C}} = \sqrt{\frac{1}{5 \times 80 \times 10^{- 6}}} = 50 r a d s^{- 1}$

$∴ ν = \frac{ω_{r}}{2 π} = \frac{50}{2 π} = 8 H z$

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Figure shows a series LCR circuit connected to a variable frequency 230 V source.The source frequency which drives the circuit in resonance is

The correct option is D 8 HzHere,L=5H,C=80μF=80×10−6F,R=40ΩVrms=230VThe resonant angular frequency is ωr=1√LC=√15×80×10−6=50rads−1∴ν=ωr2π=502π=8Hz

Figure shows a series LCR circuit connected to a variable frequency 230 V source.
The source frequency which drives the circuit in resonance is