JEE Main 2025 Apr 4 Shift 2, Physics Q10: Capacitance For Geometrical Figures With Dielectric

JEE Main2025Apr 4, Shift 2Physics

Three parallel plate capacitors $C_{1}$ , $C_{2}$ and $C_{3}$ each of capacitance $5 μ F$ 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 :

A
$22.5 μ F$
B
$7.5 μ F$
C
$9 μ F$
D
$30 μ F$

Solution

The dielectric multiplies $C_{1}$ by $K = 4$ :

$C_{1}^{'} = K \cdot C_{1} = 4 \times 5 = 20 μ F$ , while $C_{2} = C_{3} = 5 μ F$ .

$C_{1}^{'}$ and $C_{2}$ are in series along the top branch:

$C_{12} = \frac{C _{1}^{'} C _{2}}{C _{1}^{'} + C _{2}} = \frac{20 \times 5}{20 + 5} = 4 μ F$ .

This series combination is in parallel with $C_{3}$ :

$C_{e q} = C_{12} + C_{3} = 4 + 5 = 9 μ F$ .

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JEE Main 2025 Apr 4 Shift 2, Physics Q10: Capacitance For Geometrical Figures With Dielectric

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