ice_screenshot_20190305-165218.png A parallel plate capacitor is made of two square plates of side 'a', separated by a distance d The lower triangular portion is filled with a dielectric of dielectric constant K, as shown in the figure. Capacitance of this capacitor is :

Answers (1)

If K filled between the plates -

{C}'=K\frac{\epsilon _{0}A}{d}={C}'=Ck

 

 

- wherein

C\propto A

C\propto\frac{1}{d}

 

\frac{y}{x} = \frac{d}{a}

dy = \frac{d}{a} dx

dC_{1} = \frac{\varepsilon_{o}adx}{d-y} dx

dC_{2} = \frac{K\varepsilon_{o}adx}{y}

dC_{eq} =\frac{dC_{1}dC_{2}}{dC_{1}+dC_{2}} = \frac{K\varepsilon_{o}adx}{Kd + (1-K)y}

C_{eq} = \int_{0}^{a} \frac{K\varepsilon_{o}adx}{Kd + (1-K)y}

= \frac{K\varepsilon_{o}a^{2}ln K}{ d(K - 1)}

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