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Question

A parallel plate capacitor has plate area 100 m2 and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with a material of dielectric constant of 10. The resultant capacitance of the system is x pF.
The value of ε0=8.85×1012 F m1. The value of x to the nearest integer is .

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Solution

Given, Area, A=100 m2
Separation, d=10 m
Thickness, t=5 m
Dielectric constant, K=10
This capacitor can be thought as two capacitor in series, one with dilectric and another without dielectric.
C1=KAε0t,C2=Aε0dt

Ceq=C1C2C1+C2=KAε0t×AεodtKAε0t+Aεodt

Here, t=dt=5 m

Ceq=KA2ε20t2×tAε0(1+K)

Ceq=KAε0t(1+K)=10×100×8.85×10125(1+10)

Ceq=8.85×10955=0.1609090×109 F

Ceq=160.90×1012 F

Ceq=161 pF

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