JEE PYQ: Capacitance Question 33
Question 33 - 2019 (09 Jan Shift 1)
A parallel plate capacitor is made of two square plates of side ‘$a$’, separated by a distance $d$ ($d « a$). The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is:
(1) $\frac{K\epsilon_0 a^2}{2d(K+1)}$
(2) $\frac{K\epsilon_0 a^2}{d(K-1)}\ln K$
(3) $\frac{K\epsilon_0 a^2}{d}\ln K$
(4) $\frac{1}{2}\frac{K\epsilon_0 a^2}{d}$
Show Answer
Answer: (2)
Solution
From figure: $\frac{y}{x} = \frac{d}{a}$ so $y = \frac{d}{a}x$. $dC = \frac{\epsilon_0 a,dx}{\frac{y}{K} + d - y}$. Integrating: $C = \frac{K\epsilon_0 a^2 \ln K}{(K-1)d}$.
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