Two condensers of capacities C and 2C are con | vedclass

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(B) $1$. First, find the equivalent capacitance of the parallel combination of $C$ and $2C$. Since they are in parallel, $C_p = C + 2C = 3C$.$2$. Now,

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$\frac{CV}{2}$

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(B) $1$. First, find the equivalent capacitance of the parallel combination of $C$ and $2C$. Since they are in parallel, $C_p = C + 2C = 3C$.$2$. Now, this combination $(C_p = 3C)$ is in series with the third capacitor of capacity $3C$.$3$. The total equivalent capacitance $C_{eq}$ of the series combination is given by $\frac{1}{C_{eq}} = \frac{1}{3C} + \frac{1}{3C} = \frac{2}{3C}$, so $C_{eq} = \frac{3C}{2}$.$4$. The total charge $Q$ supplied by the source is $Q = C_{eq} 	imes V = \frac{3CV}{2}$.$5$. In a series circuit, the charge on each branch is the same. Thus, the charge on the $3C$ capacitor is $\frac{3CV}{2}$, and the charge on the parallel combination $(C_p = 3C)$ is also $\frac{3CV}{2}$.$6$. For the parallel combination, the voltage across both capacitors ($C$ and $2C$) is the same. Let this voltage be $V'$. $V' = \frac{Q_{parallel}}{C_p} = \frac{3CV/2}{3C} = \frac{V}{2}$.$7$. The charge on the capacitor of capacity $C$ is $q = C 	imes V' = C 	imes \frac{V}{2} = \frac{CV}{2}$.

Two condensers of capacities $C$ and $2C$ are connected in parallel and then in series with a $3^{\text{rd}}$ condenser of capacity $3C$. The combination is charged to $V$ volts. The charge on the condenser of capacity $C$ is:

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