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Inside Story

## COMMON POTENTIAL AND LOSS OF ENERGY ON SHARING CHARGES

### COMMON POTENTIAL

When two capacitors of different potential are connected by a conducting wire, then the charges flows from capacitor at higher potential to the capacitor at lower potential. This flow of **charges** continues till their potential become equal, this equal potential is called **common potential**.

Where and are capacitance of the two capacitors and and are the potential respectively.

So the common potential is given as-

From this equation, we can say that, charge lost by one capacitor is equal to **charge** gained by other capacitor.

But here you have to keep in mind that, this is not true for potential. i.e, **potential** lost by one capacitor is not equal to the potential gained by other. Because their capacitance are different.

### LOSS OF ENERGY ON SHARING OF CHARGES

When two charged **capacitors** are connected to each other, they start sharing their charges till they acquire a **common potential**. On sharing charges there is always some loss of energy. However, total charge of the system remains conserved.

Let’s consider two capacitors having capacitance and and their potential is and . Then, the total energy stored in the capacitor before the two capacitors are connected is-

(1)

When the two capacitors are connected together, the total charge on the capacitor is-

And the total **capacitance** of the two capacitors are-

Now, the total energy stored in the capacitor after they are connected is given as-

(2)

After subtracting equ(1) and equ(2), we get-

We see that, this is a positive quantity. Since U – U’ is positive, so we conclude that there is always some loss of energy, when two charged capacitors are connected together, in the form of **heat radiation** die to **electric** **current** while charging.