Question

Explain the principle of a capacitor.

Answer 1

1. Consider a metal plate P₁ having area A with some positive charge +Q be given to the plate. Let its potential be V. Its capacity is given by, C₁ = `"Q"/"V"`
2. Now consider another insulated metal plate P₂ held near plate P₁. By induction, a negative charge is produced on the nearer face and an equal positive charge develops on the farther face of P₂ as shown in figure (a) below. 
   
3. The induced negative charge lowers the potential of plate P₁, while the induced positive charge raises its potential. 
4. As the induced negative charge is closer to P₁ it is more effective, and thus there is a net reduction in the potential of plate P₁. If the outer surface of P₂ is connected to the earth, the induced positive charges on P₂ being free, flows to earth. The induced negative charge on P₂ stays on it, as it is bound to the positive charge of P₁. This greatly reduces the potential of P₂ as shown in figure (b) below.  
   
   (b)
5. If V₁ is the potential on plate P₂ due to charge (–Q) then the net potential of the system will now be +V – V₁. 
   Hence the capacity C₂ = `"Q"/("V" - "V"_1)`
   ∴ C₂ > C₁ 
6. Thus, the capacity of metal plate P₁ is increased by placing an identical earth-connected metal plate P₂ near it.