Discussion Forum



1)

 A series combination of N1 capacitors (each of capacity C1)  is charged to potential difference 3 V. Another parallel combination of N2 capacitors  (each of capacity C2) is charged to potential difference V. The total energy stored in both the combinations is same. The value of C1  in terms of C2 is 


A) $\frac{C_{2}N_{1}N_{2}}{9}$

B) $\frac{C_{2}N_{1}^{2}N_{2}^{2}}{9}$

C) $\frac{C_{2}N_{1}}{9N_{2}}$

D) $\frac{C_{2}N_{2}}{9N_{1}}$

Answer:

Option A

Explanation:

 In the first condition, 

$C_{eq}=\frac{C_{1}}{N_{1}}$

 potential difference (V) = 3 V

 $\therefore$  Energy stored ( E1) = $\frac{1}{2}CV^{2}$

 = $\frac{1}{2}(\frac{C_{1}}{N_{1}})(3V)^{2}$

   = $\frac{9}{2}\frac{C_{1}}{N_{1}}V^{2}$  .........(i)

  In the second condition,

 Ceq= N2C2, potential difference = V

 Energy stored (E2)=  $\frac{1}{2}CV^{2}$

    = $\frac{1}{2}N_{2}C_{2}V^{2}$  ........(ii)

 Accroding to the question,

  E1 = E2

 From Eqs.(i) and (ii) , we get

$\frac{9}{2}\frac{C_{1}}{N_{1}}V^{2}=\frac{1}{2}N_{2}C_{2}V^{2}$

 $C_{1}=C_{2}\frac{N_{2}N_{1}}{9}$