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(D) $1$. Analyze the circuit symmetry. The circuit consists of two parallel branches connected between points $A$ and $B$.$2$. Each branch contains a

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$2\,C$

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(D) $1$. Analyze the circuit symmetry. The circuit consists of two parallel branches connected between points $A$ and $B$.$2$. Each branch contains a combination of capacitors. Looking at the top part,there are two capacitors in parallel (capacitance $C+C = 2C$) connected in series with two other capacitors. However,by observing the symmetry,we can identify that the circuit can be simplified using the concept of equipotential points or by redrawing the circuit.$3$. The circuit is a bridge-like structure. The two capacitors in the middle are in parallel,giving $2C$. The capacitors connected diagonally are also in parallel with the outer ones.$4$. By simplifying the parallel combinations: The top two capacitors in parallel give $2C$. The bottom two capacitors in parallel give $2C$. The two diagonal capacitors are in parallel with each other,giving $2C$. $5$. Further analysis shows that the entire network simplifies to an equivalent capacitance of $2C$ between points $A$ and $B$ due to the balanced nature of the bridge.

Eight capacitors,each of capacitance $C$,are connected as shown in the figure. The effective capacitance between $A$ and $B$ is

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