Discussion Forum

 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 

Answer:

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,

 C_eq= 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

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

 $C_{1}=C_{2}\frac{N_{2}N_{1}}{9}$