Electrostatic Potential and Capacitance

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• Summary

Capacitors of capacitance C1, C2,…, Cn can be combined to obtain a system with some effective capacitance C. The effective capacitance depends on the way the individual capacitors are combined.

Combination of capacitors:

1. Capacitors in series
2. Capacitors in parallel

When capacitors are connected in parallel, the potential difference V across each is same and the charge on C₁, C₂ and C₃ is different i.e q₁, q₂ and q₃.

The total charge q is given by

q = q₁+ q₂ + q₃

the potential across each capacitor is same thus q₁ = C₁V

q₂ = C₂V and q₃ = C₃V

If C is equivalent capacitance then

q = CV

Thus CV = C₁V + C₂V + C₃V

Or

C = C₁ + C₂ + C₃

Charge on capacitor

Let two capacitors are connected in parallel, let Q be the total charge, Let Q1 be the charge on a capacitor capacity C₁ and Q₂ be the charge on a capacitor capacity C₂.
Since both capacitors have the same potential from formula V = Q/C we get,

The capacitor is said to be connected in series if the charge on each individual capacitor is same.

In this situation,

V = V₁ + V₂ + V₃

If C is the effective capacitance of combination then we know that,