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Question: Figure shows a series LCR circuit connected to a variable frequency 230 V source. <img src="https:/...

Figure shows a series LCR circuit connected to a variable frequency 230 V source.

The source frequency which drives the circuit in resonance is

A

4 Hz

B

5 Hz

C

6 Hz

D

8 Hz

Answer

8 Hz

Explanation

Solution

: Here,

L=5H,C=80μF=80×10−6F,R=40ΩL = 5H,C = 80\mu F = 80 \times 10^{- 6}F,R = 40\Omega

Vrms=230VV_{rms} = 230V

The resonant angular frequency is

ωr=1LC=15×80×10−6=50rads−1\omega_{r} = \frac{1}{\sqrt{LC}} = \frac{1}{\sqrt{5 \times 80 \times 10^{- 6}}} = 50rads^{- 1}

∴υr=ωr2π=502π=8Hz\therefore\upsilon_{r} = \frac{\omega_{r}}{2\pi} = \frac{50}{2\pi} = 8Hz