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

(a) Determine the source frequency which drives the circuit in resonance.

(b) Calculate the impedance of the circuit and amplitude of current at resonance.

(c) Show that potential drop across LC combination is zero at resonating frequency.

 

 
 
 
 
 

Answers (1)

(a) Determining the source frequency (w)

We know, w=\frac{1}{\sqrt{LC}}=\frac{1}{\sqrt{5\times 80\times 10^{-6}}}=\frac{1}{\sqrt{400\times 10^{-6}}}

                w=\frac{1000}{20}=50Hz

(b) Calculating the impedance of the given circuit and amplitude of current at resonance.

At resonance  Z=R=40\; \Omega

I^{max}_{m}=\frac{230\sqrt{2}}{R}=\frac{230\sqrt{2}}{40}=8.1\; A

(c) the potential drop across L and C,

At resonance 

X_{C}=X_{L}

iX_{C}=iX_{L}

implies that 

V_{C}=V_{L}

V_{C}-V_{L}=0     

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