Let the air filled capacitor and identical capacitor with dielectric medium having capacitance
C1 and
C2 is as shown in the figure below
Given, dielectric constant,
K=5 Since, the capacitors are connected in series, so charge on each capacitor remains same, while potential difference is distributed inversely as the ratio of capacitance, i.e.
V1:V2=: As we know, for a parallel plate capacitor, capacitance,
C=, where
A is the area of plates of capacitor and
d is the distance between the plates.
∴ For air filled capacitor,
C1=.....(i)
Similarly,
C2=.....(ii)
(
∵ the capacitors are identical)
On dividing Eq. (i) by Eq. (ii), we get
=∕ =× = or
C1:C2=1:K=1:5 ⇒V1:V2=:=5:1 OT
=⇒V1=5V2...(iii)
As,
V1+V2=12 (given)
5V2+V2=12 [from Eq. (iii)]
or
6V2=12 ⇒V2=2V and
V1=5V2=5×2=10V