Question

Two capacitors of capacitance 10 µF and 20 µF are connected in series with a 6 V battery. After the capacitors are fully charged, a slab of dielectric constant (K) is inserted between the plates of the two capacitors. How will the following be affected after the slab is introduced:

(a) The electric field energy stored in the capacitors?

(b) The charges on the two capacitors?

(c) The potential difference between the plates of the capacitors?

Justify your answer.

Answer 1

Let Q be the charge on each capacitor. So, 

Initial electric electric field energy in each capacitor becomes

Initial charge on each capacitor

where V₁ and V₂ are p.d across the capacitors

On inserting the dielectric slab the capacitance of each capacitor becomes

and equivalent capacitance becomes

New charge on the capacitor becomes

i.e., electric field energy increases in each capacitor.