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Question

The capacitance of a parallel plate capacitor becomes 43 times its original value if a dielectric slab of thickness t=d2 is inserted between the plates (where d is the distance of separation between the plates). What is the dielectric constant of the slab?
  1. K=2
  2. K=!2
  3. K=1
  4. K=2

A
K=2
B
K=!2
C
K=2
D
K=1
Solution
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The correct option is A K=2
Original value of parallel plate capacitance Co=Aϵod
Let the dielectric constant of material be K.
Capacitance of capacitor with material C1=KAϵod/2
Capacitance of capacitor without material C2=Aϵod/2
Equivalent capacitance of series combination Ceq=C1C2C1+C2=2KK+1Aϵod=2KK+1Co
Given, Ceq=43Co
We get 2KK+1=43
K=2

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