(B) The given frequency $v = \frac{1}{2\pi \sqrt{LC}}$ corresponds to the resonant frequency of a series $LCR$ circuit.At resonance,the inductive reac

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The current in the circuit is in phase with the applied $e.m.f.$ and the voltage across $R$ equals this applied $e.m.f.$

(B) The given frequency $v = \frac{1}{2\pi \sqrt{LC}}$ corresponds to the resonant frequency of a series $LCR$ circuit.At resonance,the inductive reactance $X_L = \omega L$ is equal to the capacitive reactance $X_C = \frac{1}{\omega C}$.Consequently,the net reactance $X = X_L - X_C = 0$.The impedance of the circuit $Z = \sqrt{R^2 + (X_L - X_C)^2}$ reduces to $Z = R$.Since the impedance is purely resistive,the current in the circuit is in phase with the applied $e.m.f.$Also,the voltage drop across the inductor and capacitor cancel each other out $(V_L + V_C = 0)$,meaning the entire applied $e.m.f.$ appears across the resistor $R$.

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

Medium

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

A
The quality factor of the circuit is $\omega L/R$ or $1/\omega CR$ and this is a measure of the voltage magnification (produced by the circuit at resonance) as well as the sharpness of resonance of the circuit.
B
The current in the circuit is in phase with the applied $e.m.f.$ and the voltage across $R$ equals this applied $e.m.f.$
C
The sum of the potential differences across the inductance and capacitance equals the applied $e.m.f.$ which is $180^\circ$ ahead of phase of the current in the circuit.
D
The circuit is at resonance and its impedance is made up only of a reactive part.

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Alternating Current

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

$A$ telephone wire of length $200\, km$ has a capacitance of $0.014\, \mu F$ per km. If it carries an $AC$ of frequency $5\, kHz$,what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum? (in $mH$)

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$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........
$[\pi = 3.14]$

MediumJEE MAIN 2021

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The plot given below is of the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

MediumJEE MAIN 2013

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$A$ series $LCR$ circuit is connected to a $45 \sin (\omega t) \text{ V}$ source. The resonant angular frequency of the circuit is $10^5 \text{ rad s}^{-1}$ and current amplitude at resonance is $I_0$. When the angular frequency of the source is $\omega = 8 \times 10^4 \text{ rad s}^{-1}$, the current amplitude in the circuit is $0.05 I_0$. If $L = 50 \text{ mH}$, match each entry in List-$I$ with an appropriate value from List-$II$ and choose the correct option.
List-$I$ List-$II$
$(P)$ $I_0$ in $\text{mA}$ $(1)$ $44.4$
$(Q)$ The quality factor of the circuit $(2)$ $18$
$(R)$ The bandwidth of the circuit in $\text{rad s}^{-1}$ $(3)$ $400$
$(S)$ The peak power dissipated at resonance in $\text{Watt}$ $(4)$ $2250$
$(5)$ $500$

IIT 2023

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In the circuit shown,the ratio of the quality factor to the bandwidth is: (in $\text{ s}$)

DifficultMHT CET 2023

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List-$I$	List-$II$
$(P)$ $I_0$ in $\text{mA}$	$(1)$ $44.4$
$(Q)$ The quality factor of the circuit	$(2)$ $18$
$(R)$ The bandwidth of the circuit in $\text{rad s}^{-1}$	$(3)$ $400$
$(S)$ The peak power dissipated at resonance in $\text{Watt}$	$(4)$ $2250$
	$(5)$ $500$

An alternating $e.m.f.$ of frequency $v = \frac{1}{2\pi \sqrt{LC}}$ is applied to a series $LCR$ circuit. For this frequency of the applied $e.m.f.$:

Similar Questions

$A$ telephone wire of length $200\, km$ has a capacitance of $0.014\, \mu F$ per km. If it carries an $AC$ of frequency $5\, kHz$,what should be the value of an inductor required to be connected in series so that the impedance of the circuit is minimum? (in $mH$)

$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........$[\pi = 3.14]$

The plot given below is of the average power delivered to an $LRC$ circuit versus frequency. The quality factor of the circuit is

In the circuit shown,the ratio of the quality factor to the bandwidth is: (in $\text{ s}$)

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$A$ resonance circuit having inductance and resistance $2 \times 10^{-4} \ H$ and $6.28 \ \Omega$ respectively oscillates at $10 \ MHz$ frequency. The value of the quality factor of this resonator is .........
$[\pi = 3.14]$