A parallel plate capcitor of capacitance C is charged to a potential V by a battery. Without disconencting the battery = distance between the plates of capacitor is triple and a dielectric medium of K = 10 is introduced between the plates of capacitor. Explain giving reasons how will the following be affected ?
(a) Capacitance of capacitor
(b) Charge on capacitor
(c ) Energy density of capacitor.

Explanation

(i) Using the relation `C = (in_(0)A)/(d) and K = in_(r) = 10`
and `d' = 3d`
`C_(1) = K (in_(0)A)/(3d) = 10 xx (in_(0)A)/(3d) = (10)/(3) C`
(ii) `Q = CV = (10)/(3) CV`
(iii) `U = (.^(1)//_(2) C_(1)V^(2))/(4d) rArr U = (.^(1)//_(2) C_(1)V^(2))/(3d)`
`rArr U_(1) = (.^(1)//_(2)C_(1)V^(2))/(3d) = (1)/(3) xx (1)/(2) xx (10)/(3) (CV^(2))/(Ad) = (10(1)/(2)CV^(2))/(Ad)`
`rArr` Final energy density `= (10)/(9)` Initial energy density.