a parallel plate capacitor of capacitance C is charged to potential V by a battery without disconnecting the battery distance between the places tripled and dielectric medium of K = 10 is introduced between the plates of the capacitor explained giving reasons how is the following affected capacitance of a capacitor charge on capacitor and energy density of the capacitor

Dear Student,
Given, the parallel plate capacitor has a  capacitance C.
Let the plate area be A and the distance between the plates be d.
Then,
C=εoAd
If the distance between the plates is tripled and a dielectric medium of K=10 is introduced, the capacitance will change irrespective of the fact whether or not it is connected to a battery. The new capacitance will be C' which is given by:
C'=KεoA3d=103εoAd=10C3
If earlier for a capacitance C, the charge across the plates is Q such that
Q=CV
Then, the charge developed across the capacitance C' will be
Q'=C'V=10C3V=10Q3
Ealier the energy density of the capacitor was
E=12CV2=Q22C
After the change the energy density would be
E'=12C'V2=Q'22C'E'=12×103CV2=103E
Regards

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