An initially charged undriven LCR circuit hav | vedclass

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(D) For an undriven $LCR$ circuit,the differential equation for charge $q$ is $L\frac{d^2q}{dt^2} + R\frac{dq}{dt} + \frac{q}{C} = 0$.This is a damped

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oscillate with damping,if $R^2 < \frac{4L}{C}$

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(D) For an undriven $LCR$ circuit,the differential equation for charge $q$ is $L\frac{d^2q}{dt^2} + R\frac{dq}{dt} + \frac{q}{C} = 0$.This is a damped harmonic oscillator equation.The nature of the oscillation depends on the damping factor $\frac{R}{2L}$ and the natural frequency $\omega_0 = \frac{1}{\sqrt{LC}}$.If $R^2 If $R^2 \ge \frac{4L}{C}$,the circuit is overdamped or critically damped,and no oscillations occur.Therefore,the circuit oscillates with damping if $R^2 < \frac{4L}{C}$.

List-$I$	List-$II$
$A$. Purely capacitive circuit	$I$. $I$ leads $V$ by $90^{\circ}$
$B$. Purely inductive circuit	$II$. $I$ and $V$ are in phase
$C$. $LCR$ series at resonance	$III$. $V$ leads $I$ by angle $\theta$
$D$. $LCR$ series circuit	$IV$. $V$ leads $I$ by $90^{\circ}$

An initially charged undriven $LCR$ circuit having inductance $L$,capacitance $C$ and resistance $R$ will be:

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