AIPMT 2010 Physics and Chemistry Paper

A series combination of n1 capacitors each of capacitance C1 are connected to 4V source as shown in the figure.Total capacitance of the series combination of the capacitors is
‌

1

C5

=‌

1

C1

+‌

1

C1

+‌

1

C1

+⋯...... upto n1 terms =‌

n1

C1

or Cs=‌

C1

n1

Total energy stored in a series combination of the capacitors is
us=‌

1

2

Cs(4V)2
=‌

1

2

(‌

C1

n1

)(4V)2   (using (i))...(ii)
A parallel combination of n2 capacitors each of capacitance C2 are connected to V source as shown in the figure.Total capacitance of the parallel combination of capacitors is
Cp=C2+C2+....+ upto n2 terms =n2C2
or Cc=n2C2 .......(iii)
Total energy stored in a parallel combination of capacitors is
up=‌

1

2

CpV2
=‌

1

2

(n2C2)(V)2   (Using (iii))...(iv)
According to the given problem,
Us=Up
Substituting the values of us and up from equations (ii) and (iv), we get
‌

1

2

‌

C1

n1

(4V)2=‌

1

2

(n2C2)(V)2
or ‌‌‌

C116

n1

=n2C2‌‌ or C2=‌

16C1

n1n2