A capacitor of capacitance 5 mu F is charged | vedclass

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Question

(A) Given: Capacitance $C = 5 \mu 	ext{F} = 5 	imes 10^{-6} 	ext{ F}$.Potential difference $V = 4 	ext{ V}$.Rate of change of potential difference

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$12 \mu 	ext{W}$

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(A) Given: Capacitance $C = 5 \mu 	ext{F} = 5 	imes 10^{-6} 	ext{ F}$.Potential difference $V = 4 	ext{ V}$.Rate of change of potential difference $\frac{dV}{dt} = 0.6 	ext{ Vs}^{-1}$.The energy stored in a capacitor is given by $U = \frac{1}{2}CV^2$.To find the time rate at which energy is stored,we differentiate $U$ with respect to time $t$:$\frac{dU}{dt} = \frac{d}{dt} (\frac{1}{2}CV^2) = \frac{1}{2}C \cdot 2V \cdot \frac{dV}{dt} = CV \frac{dV}{dt}$.Substituting the given values:$\frac{dU}{dt} = (5 	imes 10^{-6} 	ext{ F}) 	imes (4 	ext{ V}) 	imes (0.6 	ext{ Vs}^{-1})$.$\frac{dU}{dt} = 20 	imes 0.6 	imes 10^{-6} 	ext{ W} = 12 	imes 10^{-6} 	ext{ W} = 12 \mu 	ext{W}$.

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