(A) The resonant frequency $f_r$ of a series $LCR$ circuit is given by the formula: $f_r = \frac{1}{2\pi \sqrt{LC}}$.From this formula,it is evident t

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(A) The resonant frequency $f_r$ of a series $LCR$ circuit is given by the formula: $f_r = \frac{1}{2\pi \sqrt{LC}}$.From this formula,it is evident that the resonant frequency depends only on the inductance $L$ and the capacitance $C$ of the circuit.The resistance $R$ does not appear in the expression for the resonant frequency.Therefore,changing the resistance $R$ to $1/3$ rd of its original value will have no effect on the resonant frequency of the circuit.Thus,the resonant frequency remains unchanged.

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

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$A$ $20 \Omega$ resistance,$10 \text{ mH}$ inductance coil,and $15 \mu \text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination,the circuit resonates. If the resistance is made $1/3$ rd of its original value,the resonant frequency:

MHT CET 2025 All MHT CET

A
remains unchanged.
B
is doubled.
C
is quadrupled.
D
is halved.

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Alternating Current

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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In a series $LCR$ circuit,the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged,the new inductance should be:

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MediumMHT CET 2025

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An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

DifficultMHT CET 2026

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In a series $LCR$ circuit with $C = 2 \mu F$,$L = 1 \ mH$,and $R = 10 \ \Omega$,when the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

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In an $LRC$ series circuit at resonance,the current in the circuit is $10\sqrt{2} \ A$. If the frequency of the source is changed such that the current now lags by $45^o$ behind the applied voltage,which of the following is correct?

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$A$ $20 \Omega$ resistance,$10 \text{ mH}$ inductance coil,and $15 \mu \text{F}$ capacitor are joined in series. When a suitable frequency alternating current source is joined to this combination,the circuit resonates. If the resistance is made $1/3$ rd of its original value,the resonant frequency:

Similar Questions

In a series $LCR$ circuit,the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged,the new inductance should be:

An inductor of $0.5 \text{ mH}$, a capacitor of $20 \text{ } \mu\text{F}$ and resistance $20 \text{ } \Omega$ are connected in series with a $220 \text{ V}$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $[x]^{1/2} \text{ A}$. The value of $x$ is

In a series $LCR$ circuit with $C = 2 \mu F$,$L = 1 \ mH$,and $R = 10 \ \Omega$,when the current in the circuit is maximum,what is the ratio of the energy stored in the capacitor to the energy stored in the inductor?

In an $LRC$ series circuit at resonance,the current in the circuit is $10\sqrt{2} \ A$. If the frequency of the source is changed such that the current now lags by $45^o$ behind the applied voltage,which of the following is correct?

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