Parallel Capacitors Calculations

Let’s see parallel capacitors calculations. Capacitors connected in parallel are connected side by side and their terminals joined together so that the same applied potential difference (Pd) appears across each of them but each has a different magnitude of charge (Q) across it.

The figure below shows three capacitors connected in parallel. The same potential difference is across all of them, so that the charges on the plates have the respective magnitudes.

Q₁=C₁V,   Q₂=C₂V,  and Q₃=C₃V

In Capacitors in parallel, the same potential difference V is across all of them, but each has a certain charge on its plates whose magnitude is proportional to its capacitance.

The total charge  Q₁+Q₂+Q₃ on either the positive or negative plates of the capacitors is equal to the charge Q on the corresponding plates of the equivalent capacitor, and hence

Q=Q₁+Q₂+Q₃

but Q=CV

∴CV=C₁V+C₂V+C₃V

C=C₁+C₂+C₃…….

 For all capacitors connected in parallel, this is true

Summary Notes

1. The equivalent capacitance of capacitors connected in parallel is equal to the sum of individual capacitors’ capacitance.
2. The same potential difference appears across of them all
3. Different charge (Q) appears across each of the capacitors
4. The sum of the charge across each of the capacitors is the total charge in the circuit.

Parallel capacitors calculations

Example

Two capacitors are connected in parallel the first has 10µF and the second has 20µF capacitance and 12V potential difference (Pd) is applied across them. Calculate the equivalent capacitance of the combination, the charge on the plates of each capacitor and the energy stored in it.

Solution

The equivalent capacitance here is

C_eqv=C₁+C₂

= 10µF+20µF

= 30µF

The charges on the plates of the respective capacitors have the magnitudes;

Q₁=C₁V

The energy stored in the capacitors respectively

More energy is stored in the capacitors when they are connected in parallel across a given potential difference than when they are connected in series, because the electric fields in them are as stronger in the former case.

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Capacitors in Series Calculations / What are Capacitors / Types of Capacitors / Polarized Capacitors / Non Polarized Capacitors / Variable Capacitors