Name: Capacitance of a Parallel Plate Capacitor
Uploaded: 2019-07-19
Duration: 4 min 13 s
Description: Capacitors are available in various shapes and sizes. In this video, we will learn how to calculate the capacitance of a parallel plate capacitor.

Question

Obtain an expression for equivalent capacitance

C,

When three capacitors having capacitance

C_{1}, C_{2}

and

C_{3}

Are connected in series.

Accepted Answer

In the series combination of capacitors the first plate of the first capacitor is joined to the electric-source, the second plate is joined to the first plate of the second capacitor, the second plate of the second capacitor is joined to the first plate of third capacitor and so on, the second plate of the last capacitor being connected to the earth. In Fig., three capacitors $C_{1}, C_{2}$ and $C_{3}$ Are joined in series between points $A$ and $B$ .

Suppose, by means of the electric-source $+ Q$ Charge is given to the First plate of the first capacitor $C_{1}$ . By induction, $- Q$ Charge is produced on the inner surface of the second plate of $C_{1}$ And its free charge $+ Q$ Flows to the First plate of the second capacitor $C_{2}$ . Thus, the first plate of each capacitor has a charge $+ Q$ And the second plate has a charge $- Q$ . Let the potential differences between the plates of the capacitors $C_{1}, C_{2}$ and $C_{3}$ be $V_{1}, V_{2}$ and $V_{3}$ Respectively. Then

$V_{1} = \frac{Q}{C_{1}}, V_{2} = \frac{Q}{C_{2}}$ and $V_{3} = \frac{Q}{C_{3}}$ .

If the total potential difference between points $A$ and $B$ be $V$ , then

$V = V_{1} + V_{2} + V_{3} = \frac{Q}{C_{1}} + \frac{Q}{C_{2}} + \frac{Q}{C_{3}} . . . .((i))$

If in place of all the three capacitors, only one capacitor be placed between the points $A$ and $B$ , such that on giving it a charge $Q$ , the potential difference between its plates be $V$ , then it will be an ‘equivalent capacitor’. If the capacitance of this capacitor be $C$ , then

$V = Q / C . . . .((ii))$

Comparing equation $(i)$ and $(ii)$ , we have

$\frac{Q}{C} = \frac{Q}{C_{1}} + \frac{Q}{C_{2}} + \frac{Q}{C_{2}}$ or $\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} .$

Thus, if several capacitors are connected in series, then the reciprocal of the capacitance of the equivalent capacitor is equal to the sum of the reciprocals of the capacitances of the individual capacitors.

Obtain an expression for equivalent capacitance $C,$ When three capacitors having capacitance $C_{1}, C_{2}$ and $C_{3}$ Are connected in series.

Important Questions on Capacitors and Dielectrics

Learn and Prepare for any exam you want !

Obtain an expression for equivalent capacitance C, When three capacitors having capacitance C1, C2 and C3 Are connected in series.

Important Questions on Capacitors and Dielectrics

Learn and Prepare for any exam you want !

Obtain an expression for equivalent capacitance $C,$ When three capacitors having capacitance $C_{1}, C_{2}$ and $C_{3}$ Are connected in series.