A parallel plate capacitor with plate area A and plate separation d is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is x, where x < d. Let C₁ and C₂ be the capacitance of the system for x = 1/3d and x = 2d/3, respectively. If C₁ = 2 the value of C₂ is __________ Numerical answer type. Work it out, then open the answer.

Answer: 3. C=(ε₀A)/(d-x+x/4)=(ε₀A)/(d-3x/4) x=d/3: gap term =3d/4; x=2d/3: gap term =d/2 (C₂)/(C₁)=(3/4)/(1/2)=1.5 C₂=1.5×2=3

A parallel plate capacitor with plate area A and plate separation d… | JEE Main 2023 (6 Apr, Shift 1)

Q57JEE Main 2023 · 6 APR · SHIFT 1Medium

Dielectrics

A parallel plate capacitor with plate area $A$ and plate separation $d$ is filled with a dielectric material of dielectric constant $K = 4$ . The thickness of the dielectric material is $x$ , where $x < d$ .

Let $C_1$ and $C_2$ be the capacitance of the system for $x = \frac{1}{3}d$ and $x = \frac{2d}{3}$ , respectively. If $C_1 = 2\mu\text{F}$ the value of $C_2$ is __________ $\mu\text{F}$

Numerical answer type. Work it out, then open the answer.

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Answer: 3

$C=\frac{\epsilon_0A}{d-x+\frac{x}{4}}=\frac{\epsilon_0A}{d-\frac{3x}{4}}$
$x=\frac{d}{3}$ : gap term $=\frac{3d}{4}$ ; $x=\frac{2d}{3}$ : gap term $=\frac{d}{2}$
$\frac{C_2}{C_1}=\frac{3/4}{1/2}=1.5$
$C_2=1.5\times2=3\ \mu\text{F}$

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