Question

A parallel plate capacitor with plate separation 5mm is charged by a battery . It is found that on introducing a mica sheet 2mm thick ,While keeping the battery connections intact. The capacitor draws 25% more energy from the battery than before. Find dielectric constant of mica

Answer 1

Given: A parallel plate capacitor with plate separation 5 mm, a mica sheet 2 mm thick.

To find: dielectric constant of mica?

Solution:

• Now we have given that on introducing a mica sheet 2 mm thick the capacitor draws 25% more energy from the battery than before.

• So Q = 25% of initial Q

             Q = 1.25Q(1)

• Now C = 1.25Q(1)V

                C = 1.25 C(1)

• Now we know that when a dielectric is introduced, then:

             C = ∈oA / d - t(1-1/k)

• We can rewrite it as:

             C = ( ∈oA/d ) / ( 1 - t(1-1/k)/d )

             C = ( C1 ) / ( 1 - t(1-1/k)/d )

• Now putting the values in formula, we get:

             1.25 C(1) = ( C1 ) / ( 1 - 2(1-1/k)/5 )

             1.25( 1 -  2/5 + 2/5k ) = 1

             2/ 5k = 1/1.25 - 1 + 2/5

             2/ 5k = 1 / 5

             k = 2

Answer:

           So the dielectric constant is 2.