A parallel plate capacitor of area ' A ' plate separation ' d ' is filled with two d

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2. Electric Potential and Capacitance

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A parallel plate capacitor of area ' $A$ ' plate separation ' $d$ ' is filled with two dielectrics as shown. What is the capacitance of the arrangement?

A

$\frac{3 K \varepsilon_0 A}{4 d}$

B

$\frac{4 K \varepsilon_0 A}{3 d}$

C

$\frac{(K+1) \varepsilon_0 A}{2 d}$

D

$\frac{K(K+3) \varepsilon_0 A}{2(K+1) d}$

Solution

(c)

$c_1=\frac{(A / 2) \varepsilon_0}{d / 2}=\frac{A \varepsilon_0}{d}, c_2=K \frac{A \varepsilon_0}{d}, c_3=K \frac{A \varepsilon_0}{2 d}$

$\therefore \quad c_{e q .}=\frac{c_1 \times c_2}{c_1+c_2}+c_3=\frac{(3+ K ) K A \varepsilon_0}{2 d( K +1)}$

$\left(\because C_1\right.$ and $C_2$ are in series and resultant of these two in parallel with $C_3$ )

Standard 12

Physics

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