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Answer please! 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

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 :

 

  • Option 1)

    \frac{K\epsilon _{0}a^{2}}{2d(K+1)}\; \;

  • Option 2)

    \; \frac{K\epsilon _{0}a^{2}}{d(K-1)}1n\, K\; \;

  • Option 3)

    \;\frac{K\epsilon _{0}a^{2}}{d}1n\, K\; \;

  • Option 4)

    \;\frac{1}{2}\frac{K\epsilon _{0}a^{2}}{d}\; \; \;

Answers (1)
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A admin

 

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)}

 


Option 1)

\frac{K\epsilon _{0}a^{2}}{2d(K+1)}\; \;

Option 2)

\; \frac{K\epsilon _{0}a^{2}}{d(K-1)}1n\, K\; \;

Option 3)

\;\frac{K\epsilon _{0}a^{2}}{d}1n\, K\; \;

Option 4)

\;\frac{1}{2}\frac{K\epsilon _{0}a^{2}}{d}\; \; \;

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