First slide

Capacitance

Question

A parallel plate capacitor (condenser) has a certain capacitance (capacity). When 2/3 rd of the distance between the plates is filled with a dielectric, the (capacity) capacitance is found to be 2.25 times the initial capacitance. The dielectric constant of the dielectric

Moderate

A

1
B

3
C

7
D

6

Solution

C = 2.25C₀ $\Rightarrow$
$\frac{2.25 {Aε}_{0}}{d} = \frac{{Aε}_{0}}{d - \frac{2}{3} d (1 - \frac{1}{K})} = \frac{{Aε}_{0}}{d - \frac{2 d}{3} + \frac{2 d}{3 K}} \frac{1}{\frac{d}{3} + \frac{2 d}{3 K}} = \frac{2.25}{d} = \frac{3 K}{d (K + 2)}$
$\Rightarrow$ 2.25K + 4.5 = 3K $\Rightarrow$ 0.75K = 4.5
$K = \frac{4.5}{0.75} = \frac{450}{75} = 6$

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