Name: Equipotential Surfaces and Its Properties
Uploaded: 2019-07-19
Duration: 7 min 22 s
Description: The surface over which the electric potential is the same everywhere is called an equipotential surface. Let's more about it and its properties in this video.

Question

Define capacitor. Draw a circuit diagram and obtain a relation for equivalent capacitance for the series combination of three capacitors.

Accepted Answer

Capacitor is an electrical system capable of storing electrical charge (electrical energy). It comprises of a single or two conductors carrying equal and opposite charge and separated by a potential. Its SI unit is farad (F). It is defined as the ratio of charge stored to the potential difference between the conductors.

$C = \frac{Q}{V}$

Consider the circuit shown in the attached figure with two capacitors in series.
In series, charge across the capacitors is same. Also, the charge across the equivalent capacitor is also the same.

$Q_{1} = Q_{2} = Q_{3} = Q . . . . . . . (i)$

Using Kirchhoffs Voltage Law, $V = V_{1} + V_{2} + V_{3} . . . . . . . . . . . . . . . . (i i)$

Using definition of capacitance,

$C_{e q} = Q V . . . . . . . . . . . . . (i i i) C_{1} = Q V_{1} . . . . . . . . . . . . . . . . (i v) C_{2} = Q V_{2} . . . . . . . . . . . . . . . . (v) C_{3} = Q V_{3 . . . . . . . . . . . . . . (V i)}$

Substituting (iii), (iv), (v), (vi), in (ii), we get,

$\frac{Q}{C_{e q}} = \frac{Q}{C_{1}} + \frac{Q}{c_{2}} + \frac{Q}{C_{3}} \frac{1}{C_{e q}} = \frac{1}{C_{1}} + \frac{1}{c_{2}} + \frac{1}{C_{3}}$

Here is our required answer.

Define capacitor. Draw a circuit diagram and obtain a relation for equivalent capacitance for the series combination of three capacitors.

Important Questions on Electrostatic Potential and Capacitance

Learn and Prepare for any exam you want !