A parallel plate capacitor with plate area and plate separation is filled with a dielectric material of dielectric constant K = 4. The thickness of the dielectric material is . where . [2023]

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Solution

Q.
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 $x = \frac{2 d}{3}$ respectively. If $C_{1} = 2 μ F$ , the value of $C_{2}$ is ________ $μ F$ . [2023]

Ans.
(3)

$For x = \frac{d}{3}$

$C_{1} = \frac{ε_{0} A}{(\frac{d / 3}{k} + \frac{2 d}{3})} = \frac{ε_{0} A}{\frac{d}{12} + \frac{2 d}{3}} = \frac{ε_{0} A}{d} \times \frac{12}{9}$

$C_{1} = \frac{4}{3} \frac{ε_{0} A}{d} = 2 μ F$

$For x = \frac{2 d}{3}$

$C_{2} = \frac{ε_{0} A}{(\frac{2 d / 3}{k} + \frac{d}{3})} = \frac{ε_{0} A}{d} \times 2 = \frac{6}{4} \times 2 = 3 μ F$

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