A parallel plate capacitor with air between plates has a capacitance of 9 pF . separation between it

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1. Electric Charges and Fields

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A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$. The separation between its plates is '$d$'. The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac{2d}{3}$. Capacitance of the capacitor is now........$pF$

A

$18$

B

$25$

C

$81$

D

$20$

Solution

$C_{1}=\frac{K_{1} \in_{0} A}{\left(\frac{d}{3}\right)}, C_{2}=\frac{K_{2} \in_{0} A}{\left(\frac{2 d}{3}\right)}, \frac{E_{0} A}{d}=9,$

$C_{e q .}=\frac{C_{1} C_{2}}{C_{1}+C_{2}}$

Standard 12

Physics

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