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(D) $1$. Identify the parallel combination between points $C$ and $D$: The capacitors $2\, \mu F$,$5\, \mu F$,and $5\, \mu F$ are connected in paralle

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$2.4$

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(D) $1$. Identify the parallel combination between points $C$ and $D$: The capacitors $2\, \mu F$,$5\, \mu F$,and $5\, \mu F$ are connected in parallel. Their equivalent capacitance $C_{CD}$ is given by $C_{CD} = 2 + 5 + 5 = 12\, \mu F$.$2$. Identify the parallel combination between points $E$ and $B$: The capacitors $4\, \mu F$ and $2\, \mu F$ are connected in parallel. Their equivalent capacitance $C_{EB}$ is given by $C_{EB} = 4 + 2 = 6\, \mu F$.$3$. Now,the circuit simplifies to three capacitors in series: $6\, \mu F$ (connected to $A$),$C_{CD} = 12\, \mu F$,and $C_{EB} = 6\, \mu F$.$4$. The equivalent capacitance $C_{eq}$ between $A$ and $B$ for series connection is given by $\frac{1}{C_{eq}} = \frac{1}{6} + \frac{1}{12} + \frac{1}{6}$.$5$. Calculating the sum: $\frac{1}{C_{eq}} = \frac{2 + 1 + 2}{12} = \frac{5}{12}$.$6$. Therefore,$C_{eq} = \frac{12}{5} = 2.4\, \mu F$.

The equivalent capacitance between $A$ and $B$ in the circuit given below is.....$\mu F$

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