Three parallel plate capacitors C_1, C_2 and C_3 each of capacitance 5 \mu ~F are connected as shown in figure. The effective capacitance between points A and B , when the space between the parallel plates of C_1 capacitor is filled with a dielectric medium having dielectric constant of 4, is :

Capacitor PYQ — JEE Main 2025 · 4 Apr · Shift 2 · Q62 with Solution

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Correct answer: A

Capacitance after inserting dielectric in $C_1$

Initially, each capacitor has capacitance $C_1=C_2=C_3=5\,\mu F.$

When a dielectric of dielectric constant $K=4$ is inserted fully in $C_1$ , $C_1' = K C_1 = 4\times 5 = 20\,\mu F.$
Use the given circuit arrangement

From the figure, $C_2$ and $C_3$ are in series, and that series combination is in parallel with $C_1'$ between $A$ and $B$ .
Series combination of $C_2$ and $C_3$
$= \frac{5\times 5}{5+5} = \frac{25}{10} = 2.5\,\mu F.$$$
Parallel combination with $C_1'$

Since this is in parallel with $C_1' = 20\,\mu F$ , $C_{\text{eq}} = C_1' + C_{23} = 20 + 2.5 = 22.5\,\mu F.$
Check options

Therefore, the effective capacitance is $\boxed{22.5\,\mu F}.$

This corresponds to Option D.
Comparison with stored answer

The stored correct answer is A: $9\,\mu F$ , but our derived answer is D: $22.5\,\mu F$ .

Hence, I do not agree with the stored answer. The stored answer is likely incorrect unless the circuit figure corresponds to a different connection than the usual one inferred here.