(A) In a series $LCR$ circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Resonance occurs when the inductive reactance $X_L = \ome

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(A) In a series $LCR$ circuit,the impedance $Z$ is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$.Resonance occurs when the inductive reactance $X_L = \omega L$ and capacitive reactance $X_C = \frac{1}{\omega C}$ are equal and opposite,such that $X_L - X_C = 0$.At this condition,the impedance $Z$ becomes minimum $(Z = R)$,and the current $I = \frac{V}{Z}$ becomes maximum.Since the condition for resonance is indeed $X_L = X_C$,the Reason correctly explains the Assertion.

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

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Assertion: In a series $LCR$ circuit,resonance can take place.
Reason: Resonance takes place if inductive and capacitive reactances are equal and opposite.

AIIMS 1998 All AIIMS

A
If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
B
If both Assertion and Reason are correct but Reason is not a correct explanation of the Assertion.
C
If the Assertion is correct but Reason is incorrect.
D
If both the Assertion and Reason are incorrect.

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Half Power Frequency , Quality Factor ,Resonance in AC Circuit

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Assertion: In a series $LCR$ circuit,resonance can take place.Reason: Resonance takes place if inductive and capacitive reactances are equal and opposite.

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The resonant frequency of a series $LCR$ circuit is $f_R$. The circuit is connected to a sinusoidally alternating e.m.f. of frequency $2 f_R$. The inductive reactance becomes $X_{L_1}$ and capacitive reactance becomes $X_{C_1}$ after changing the frequency. $X_{C_1}$ is equal to:

$A$ series $LCR$ circuit with inductance $L = 10\,H$,capacitance $C = 10\,\mu F$,and resistance $R = 50\,\Omega$ is connected to an $AC$ source of voltage $V = 200 \sin(100t)\,V$. If the resonant frequency of the $LCR$ circuit is $\nu_{0}$ and the frequency of the $AC$ source is $\nu$,then:

When resonance is produced in a series $LCR$ circuit,then which of the following is not correct?

The reading of the ammeter in the following circuit is (in $A$)

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Assertion: In a series $LCR$ circuit,resonance can take place.
Reason: Resonance takes place if inductive and capacitive reactances are equal and opposite.