Two capacitors of capacitance and 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:

Question

Two capacitors of capacitance and 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.

Philoid · Accepted Answer

Let the capacitances be and

The battery has a potential of .

(a) The electric field energy values before the slab was inserted is

the insertion of the slab increases the capacitances as and

The electric field energy values after the slab of dielectric constant (K) is inserted is

(b) In series connection, charges across each capacitor is same.

Old charge configuration=

New charge configuration=

(C) Potential difference change according to the capacitance. The new potential differences would be and .

Here, we have assumed that the battery is not disconnected.