(C) The resonant frequency $f_r$ of a series $LCR$ circuit is given by the formula:$f_r = \frac{1}{2 \pi \sqrt{LC}}$To increase the resonant frequency

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Another capacitor should be added in series with the first capacitor

(C) The resonant frequency $f_r$ of a series $LCR$ circuit is given by the formula:$f_r = \frac{1}{2 \pi \sqrt{LC}}$To increase the resonant frequency $f_r$,the product $LC$ must decrease.When a capacitor is added in series with the existing capacitor,the equivalent capacitance $C_{eq}$ is given by $\frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2}$. This results in a decrease in the total capacitance $(C_{eq} Since $f_r \propto \frac{1}{\sqrt{C}}$,a decrease in total capacitance leads to an increase in the resonant frequency.

Class 12 Physics Alternating Current Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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To increase the resonant frequency in a series $LCR$ circuit,

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A
Source frequency should be increased
B
Another resistance should be added in series with the first resistance
C
Another capacitor should be added in series with the first capacitor
D
Another inductor should be added in series with the first inductor

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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The output voltage (taken across the resistance) of an $L-C-R$ series resonant circuit falls to half its peak value at a frequency of $200 \,Hz$ and again reaches the same value at $800 \,Hz$. The bandwidth of this circuit is ............. $\,Hz$.

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$A$ resistor of $50 \Omega$,an inductor of self-inductance $\left(\frac{3}{\pi^2}\right) H$,and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \ V$ and $50 \ Hz$. When the voltage and current are in phase,the value of capacitance is (nearly):

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To increase the resonant frequency in a series $LCR$ circuit,

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In a series resonant $LCR$ circuit,the voltage across $R$ is $100 \ V$ and $R = 1 \ k\Omega$ with $C = 2 \ \mu F$. The resonant frequency $\omega$ is $200 \ rad/s$. At resonance,the voltage across $L$ is:

In a series $LCR$ circuit,the plot of $I_{max}$ vs $\omega$ is shown in the figure. Find the bandwidth and mark it in the figure.

In a series $LCR$ circuit,$C = 2 \mu F$,$L = 1 \text{ mH}$,and $R = 10 \Omega$. The ratio of the energies stored in the inductor and the capacitor,when the maximum current flows in the circuit,is:

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$A$ resistor of $50 \Omega$,an inductor of self-inductance $\left(\frac{3}{\pi^2}\right) H$,and a capacitor of unknown capacity are connected in series to an a.c. source of $100 \ V$ and $50 \ Hz$. When the voltage and current are in phase,the value of capacitance is (nearly):

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