You drive a series RLC circuit with a function generator, the voltage across and

Question

You drive a series RLC circuit with a function generator, the voltage across and current through which are plotted below. Which of the following statements accurately describes the situation The capacitor is dominating the circuit behavior, you are driving below the circuit's resonance frequency. The capacitor is dominating the circuit behavior, you are driving above the circuit's resonance frequency. The inductor is dominating the circuit behavior, you are driving above the circuit's resonance frequency. The inductor is dominating the circuit behavior, you are driving below the circuit's resonance frequency. None of the above.

Explanation / Answer

in an RLC series circuit, resonant frequency is given as 1/(2*pi*sqrt(L*C))

at any frequency f, capacitive reactance is Xc=-j/(2*pi*f*C)

and inductive reactance=j*2*pi*f*C

for frequencies below resonant frequency, that is when

f<1/(2*pi*sqrt(L*C))

==>f^2<1/(4*pi^2*L*C)

==>f*2*pi*L<1/(2*pi*f*C)

==>|Xc| > |Xl|

where | | denotes the absolute value.

hence the inductance is capacitive in nature

in that case current=voltage/total reactance

will be leading voltage source.

(because capacitive means phase angle is negative. so when it goes in the denominator, phase angle become positive for the current)

in the given figure, as current is ahead of the voltage in phase, frequency is below the resonant frequency and capacitor is dominant in the circuit.

hence option A is correct.

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