In the circuit shown in the figure,four capac | vedclass

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(D) The circuit consists of two branches connected in parallel across the $10 \ 	ext{V}$ battery. Branch $1$ consists of $10 \ \mu	ext{F}$ and $4 \

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$20$

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(D) The circuit consists of two branches connected in parallel across the $10 \ 	ext{V}$ battery. Branch $1$ consists of $10 \ \mu	ext{F}$ and $4 \ \mu	ext{F}$ capacitors in series. The equivalent capacitance is $C_1 = \frac{10 	imes 4}{10 + 4} = \frac{40}{14} = \frac{20}{7} \ \mu	ext{F}$. The charge on this branch is $Q_1 = C_1 V = \frac{20}{7} 	imes 10 = \frac{200}{7} \ \mu	ext{C}$. Branch $2$ consists of $5 \ \mu	ext{F}$ and $6 \ \mu	ext{F}$ capacitors in series. The equivalent capacitance is $C_2 = \frac{5 	imes 6}{5 + 6} = \frac{30}{11} \ \mu	ext{F}$. The charge on this branch is $Q_2 = C_2 V = \frac{30}{11} 	imes 10 = \frac{300}{11} \ \mu	ext{C}$. Since the $5 \ \mu	ext{F}$ capacitor is in series with the $6 \ \mu	ext{F}$ capacitor in the second branch,the charge on the $5 \ \mu	ext{F}$ capacitor is equal to the total charge on that branch,which is $Q_2 = \frac{300}{11} \approx 27.27 \ \mu	ext{C}$. Wait,re-evaluating the circuit: The nodes $A$ and $C$ are connected to the battery. The capacitors $10 \ \mu	ext{F}$ and $5 \ \mu	ext{F}$ are connected to node $A$. The capacitors $4 \ \mu	ext{F}$ and $6 \ \mu	ext{F}$ are connected to node $C$. Node $B$ is the junction. This is a Wheatstone bridge. Let $V_A = 10 \ 	ext{V}$ and $V_C = 0 \ 	ext{V}$. Let $V_B$ be the potential at node $B$. Using Kirchhoff's Current Law at node $B$: $(V_B - 10) 	imes 10 + (V_B - 10) 	imes 5 + (V_B - 0) 	imes 4 + (V_B - 0) 	imes 6 = 0$. $15(V_B - 10) + 10V_B = 0 \implies 25V_B = 150 \implies V_B = 6 \ 	ext{V}$. The potential difference across the $5 \ \mu	ext{F}$ capacitor is $V_A - V_B = 10 - 6 = 4 \ 	ext{V}$. The charge on the $5 \ \mu	ext{F}$ capacitor is $Q = C \Delta V = 5 \ \mu	ext{F} 	imes 4 \ 	ext{V} = 20 \ \mu	ext{C}$.

In the circuit shown in the figure,four capacitors are connected to a battery. The charge on the $5 \ \mu\text{F}$ capacitor is ....... $\mu\text{C}$.

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