Mention the factors on which the resonant frequency of a series LCR…

Mention the factors on which the resonant frequency of a series LCR circuit depends. Plot a graph showing variation of impedance of a series LCR circuit with the frequency of the applied a.c. source.

Ans.

Factors affecting the resonant frequency of a series LCR circuit:

1. Inductance (L): Higher inductance lowers the resonant frequency.

2. Capacitance (C): Higher capacitance increases the resonant frequency.

3. Resistance (R): Higher resistance broadens the resonance curve and reduces the amplitude of the current at resonance.

4. Quality factor (Q): Higher Q factors indicate sharper resonance peaks and narrower bandwidths.

The resonant frequency �0f0​ of a series LCR circuit: �0=12���f0​=2πLC​1​

To plot the variation of impedance of a series LCR circuit with the frequency of the applied AC source:

1. Choose a range of frequencies $f$ for the x-axis.

2. Calculate the inductive reactance ��XL​ and capacitive reactance ��XC​ for each frequency.

3. Use the impedance formula �=�2+(��−��)2Z=R2+(XL​−XC​)2​ to calculate the impedance $Z$ for each frequency.

4. Plot the impedance $Z$ against the frequency $f$.

The resulting graph typically shows a peak at the resonant frequency �0f0​, where the impedance is minimized. As the frequency deviates from the resonant frequency, the impedance increases due to the combined effects of inductive and capacitive reactance.