KEAM 2021 Physics and Chemistry Solved Paper

Let the air filled capacitor and identical capacitor with dielectric medium having capacitance C1 and C2 is as shown in the figure belowGiven, 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=‌

1

C1

:‌

1

C2

As we know, for a parallel plate capacitor, capacitance, C=‌

ε0A

d

, where A is the area of plates of capacitor and d is the distance between the plates.
∴ For air filled capacitor, C1=‌

ε0A

d

.....(i)
Similarly, C2=‌

Kε0A

d

.....(ii)
( ∵ the capacitors are identical)
On dividing Eq. (i) by Eq. (ii), we get
‌

C1

C2

=‌

ε0A

d

∕‌

Kε0A

d

=‌

ε0A

d

×‌

d

Kε0A

=‌

1

K

or ‌‌C1:C2=1:K=1:5
⇒‌‌V1:V2=‌

1

C1

:‌

1

C2

=5:1
OT ‌

V1

V2

=‌

5

1

⇒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