Find the charge on capacitor C_3. Given that | vedclass

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Question

(A) The circuit consists of two parallel branches connected across a potential difference $V$.Branch $1$ contains capacitors $C_1$ and $C_2$ in series

Vedclass · Accepted Answer

$\frac{3}{2} CV$

Vedclass · Answer

(A) The circuit consists of two parallel branches connected across a potential difference $V$.Branch $1$ contains capacitors $C_1$ and $C_2$ in series. The equivalent capacitance of this branch is $C_{eq1} = \frac{C_1 C_2}{C_1 + C_2} = \frac{C \cdot C}{C + C} = \frac{C}{2}$.The charge on this branch is $q_1 = C_{eq1} V = \frac{CV}{2}$.Branch $2$ contains capacitors $C_3$ and $C_4$ in series. The equivalent capacitance of this branch is $C_{eq2} = \frac{C_3 C_4}{C_3 + C_4} = \frac{3C \cdot 3C}{3C + 3C} = \frac{9C^2}{6C} = \frac{3}{2} C$.The charge on this branch is $q_2 = C_{eq2} V = \frac{3}{2} CV$.Since $C_3$ and $C_4$ are in series,the charge on each capacitor in that branch is the same as the total charge on the branch.Therefore,the charge on capacitor $C_3$ is $q_2 = \frac{3}{2} CV$.

Find the charge on capacitor $C_3$. Given that $C_1 = C_2 = C$ and $C_3 = C_4 = 3C$.

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