A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ((1/3))rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

### Related Formula Alternatively, treat as two capacitors in series: Ceq = (C1 C2/C1 + C2) ### Core Logic Initial capacitance (vacuum): C = A epsilon0d. The system can be modelled as two capacitors in series: 1. A vacuum capacitor of thickness d - (d/3) = (2d/3) 2. A dielectric capacitor of thickness (d/3) and dielectric constant K. ### Step 1: Capacitors in Series The capacitances are: Now, equivalent capacitance in series: ### Pattern Recognition Partial dielectric filling of thickness t: Use formula Cnew = (epsilon0 A/d - t + t/K). Plugging t = d/3 directly gives (epsilon0 A/d - d/3 + d/3K) = (epsilon0 A/2d)3 + (d/3K) = (3K epsilon0 A/2Kd + d) = (3KC/2K+1). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electrostatics

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ((1/3))rd of the separation between the plates and relative permittivity K is in

### Related Formula Alternatively, treat as two capacitors in series: Ceq = (C1 C2/C1 + C2) ### Core Logic Initial capacitance (vacuum): C = A epsilon0d. The system can be modelled as two capacitors in series: 1. A vacuum capacitor of thickness d - (d/3) = (2d/3) 2. A dielectric capacitor of thickness (d/3) and dielectric constant K. ### Step 1: Capacitors in Series The capacitances are: Now, equivalent capacitance in series: ### Pattern Recognition Partial dielectric filling of thickness t: Use

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ((1/3))rd of the separation between the plates and relative permittivity K is introduced between the plates. The new capacitance of the system is :

### Related Formula Alternatively, treat as two capacitors in series: Ceq = (C1 C2/C1 + C2) ### Core Logic Initial capacitance (vacuum): C = A epsilon0d. The system can be modelled as two capacitors in series: 1. A vacuum capacitor of thickness d - (d/3) = (2d/3) 2. A dielectric capacitor of thickness (d/3) and dielectric constant K. ### Step 1: Capacitors in Series The capacitances are: Now, equivalent capacitance in series: ### Pattern Recognition Partial dielectric filling of thickness t: Use formula Cnew = (epsilon0 A/d - t + t/K). Plugging t = d/3 directly gives (epsilon0 A/d - d/3 + d/3K) = (epsilon0 A/2d)3 + (d/3K) = (3K epsilon0 A/2Kd + d) = (3KC/2K+1). ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 12 Physics: Electrostatics

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness ((1/3))rd of the separation between the plates and relative permittivity K is in

### Related Formula Alternatively, treat as two capacitors in series: Ceq = (C1 C2/C1 + C2) ### Core Logic Initial capacitance (vacuum): C = A epsilon0d. The system can be modelled as two capacitors in series: 1. A vacuum capacitor of thickness d - (d/3) = (2d/3) 2. A dielectric capacitor of thickness (d/3) and dielectric constant K. ### Step 1: Capacitors in Series The capacitances are: Now, equivalent capacitance in series: ### Pattern Recognition Partial dielectric filling of thickness t: Use

A parallel plate capacitor has capacitance C, when there is vacuum within the parallel plates. A sheet having thickness…

Year	2026	2025	2024	Total
Questions	24	39	16	79

Year

2026

2025

2024

Total

Questions

Solution & Explanation

Related Formula

C = (ε₀ A)/(d - t + (t)/(K))

Alternatively, treat as two capacitors in series: $Ceq = (C₁ C₂)/(C₁ + C₂)$ $C_{eq} = \frac{C_1 C_2}{C_1 + C_2}$

Core Logic

Initial capacitance (vacuum): $C = A ε₀d$ $C = \frac{A \epsilon_{0}}{d}$.

Capacitance with Dielectric diagram for Q34 - JEE Main 2026 Morning

The system can be modelled as two capacitors in series:

A vacuum capacitor of thickness $d - (d)/(3) = (2d)/(3)$ $d - \frac{d}{3} = \frac{2d}{3}$
A dielectric capacitor of thickness $(d)/(3)$ $\frac{d}{3}$ and dielectric constant $K$ $K$.

Step 1: Capacitors in Series

The capacitances are:

C₁ = (ε₀ A)/(((2d)/(3))) = (3)/(2) ((ε₀ A)/(d)) = (3)/(2) C

C₂ = (K ε₀ A)/(((d)/(3))) = 3K ((ε₀ A)/(d)) = 3KC

Now, equivalent capacitance in series:

Ceq = (C₁ C₂)/(C₁ + C₂) = (((3)/(2) C) \times (3KC))/((3)/(2) C + 3KC)

Ceq = ((9)/(2)KC²)/((3)/(2)C(1 + 2K))

Ceq = (3KC)/(2K + 1)

Pattern Recognition

Partial dielectric filling of thickness $t$ $t$: Use formula $Cnew = (ε₀ A)/(d - t + t/K)$ . Plugging $t = d/3$ $t = d/3$ directly gives $(ε₀ A)/(d - d/3 + d/3K) = (ε₀ A)/((2d)/(3) + (d)/(3K)) = (3K ε₀ A)/(2Kd + d) = (3KC)/(2K+1)$ .

Chapter Mix

Class 12 Physics: Electrostatics

More Electrostatics Previous-Year Questions

Q45 jee_main_2026_21_jan_morning Electric Potential Energy

A point charge of

10⁻⁸

C is placed at origin. The work done in moving a point charge 2

μ

C from point A(4, 4, 2) m to B(2, 2, 1) m is ____ J.

( 14πε₀=9\times10⁹ in SI units)

A. $45 \times 10⁻⁶$ $45 \times 10^{-6}$
B. $0$ $0$
C. $30 \times 10⁻⁶$ $30 \times 10^{-6}$
D. $15 \times 10⁻⁶$ $15 \times 10^{-6}$