Capacitor related doubt

Question

When two capacitors are joined one charged and other uncharged.
how to calculate energy ? Please show the calculation part also

Answer 1

Let C₁ be the charged capacitor and C₂ be the uncharged capacitor.

 

Initial charge Q₀ on C₁ is: Q₀=C₁V₀ being V₀ the initial voltage across C1.

Initial energy stored in C₁=(1/2)Q₀V₀

 

When you connect both capacitors in parallel C₁ transfers some of its charge to C₂.

By the conservation of charge principle the final charge Q₁ on C₁ + final charge Q₂ on C₂ = Initial charge Q₀ on C₁ and the voltage V across both capacitors is the same (they are in parallel).

 

So you have:

 

Q₁ + Q₂ = Q₀ 

Q₁ = C₁V

Q₂ = C₂V

 

which you can solve for V and then obtain the values of Q₁ and Q₂ 

 

The final energy of the two capacitors system = (1/2)Q₁V+ (1/2)Q₂V which you will find is less than the initial energy stored at C₁due to heat and electromagnetic losses.