Effective capacitance of parallel combination | vedclass

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Question

(C) For parallel combination,the effective capacitance is $C_{p} = C_{1} + C_{2} = 10\; \mu F$. Energy stored in a capacitor is given by $U = \frac{1}

Vedclass · Accepted Answer

$1.6$

Vedclass · Answer

(C) For parallel combination,the effective capacitance is $C_{p} = C_{1} + C_{2} = 10\; \mu F$. Energy stored in a capacitor is given by $U = \frac{1}{2}CV^{2}$. Given that when connected to the same voltage $V$,$U_{2} = 4U_{1}$. Substituting the formula,$\frac{1}{2}C_{2}V^{2} = 4 	imes \frac{1}{2}C_{1}V^{2}$,which simplifies to $C_{2} = 4C_{1}$. Substituting $C_{2} = 4C_{1}$ into the parallel equation: $C_{1} + 4C_{1} = 10\; \mu F \implies 5C_{1} = 10\; \mu F \implies C_{1} = 2\; \mu F$. Then,$C_{2} = 4 	imes 2 = 8\; \mu F$. For series combination,the effective capacitance $C_{s}$ is given by $\frac{1}{C_{s}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} = \frac{C_{1} + C_{2}}{C_{1}C_{2}}$. $C_{s} = \frac{C_{1}C_{2}}{C_{1} + C_{2}} = \frac{2 	imes 8}{2 + 8} = \frac{16}{10} = 1.6\; \mu F$.

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