7 Combination of Capacitors Energy Stored in a Capacitor

Combination of Capacitors Energy Stored in a Capacitor

Combination of Capacitors

Capacitors in series

• Capacitors are said to be connected in series when the potential difference applied across their combination is the sum of the resulting potential differences across each capacitor.
• Also in series combination the charge in all of the capacitors is same.

The potential difference across the separate capacitors are given by,

However, the potential difference across the series combination of capacitor is V volt.

∴ V = V₁ + V₂ + V₃ (i)

Let C_s represent the equivalent capacitance. Then,

Combining (i) and (ii), we obtain

Capacitors in parallel 

Capacitors are said to be connected in parallel when a potential difference that is applied across their combination results in the same across each capacitor.

• If Q is the total charge on the parallel network, then

Let C_P be the equivalent capacitance of the parallel combination.

Now, Q = C_PV

Q₁ = C₁V, Q₂ = C₂V, and Q₃ = Q₃V (ii)

Combining (i) and (ii), we obtain

C_PV = C₁V + C₂V + C₃V

Energy Stored in a Charged Capacitor

The energy of a charged capacitor is measured by the total work done in charging the capacitor to a given potential.

Let us assume that initially both the plates are uncharged. Now, we have to repeatedly remove small positive charges from one plate and transfer them to the other plate.

Let

q → Total quantity of charge transferred

V → Potential difference between the two plates

Then,

q = CV

Now, when an additional small charge dq is transferred from the negative plate to the positive plate, the small work done is given by,

The total work done in transferring charge Q is given by,

This work is stored as electrostatic potential energy U in the capacitor.