Learning Objectives

➣ Capacitor

➣ Capacitance

➣ Capacitance of an Isolated Sphere

➣ Spherical Capacitor

➣ Parallel-plate Capacitor

➣ Special Cases of Parallel- plate Capacitor

➣ Multiple and Variable Capacitors

➣ Cylindrical Capacitor

➣ Potential Gradient in Cylindrical Capacitor

➣ Capacitance Between two Parallel Wires

➣ Capacitors in Series

➣ Capacitors in Parallel

➣ Cylindrical Capacitor with Compound Dielectric

➣ Insulation Resistance of a Cable Capacitor

➣ Energy Stored in a Capacitor

➣ Force of Attraction Between Oppositely-charged Plates

➣ Current-Voltage

Relationships in a Capacitor

➣ Charging of a Capacitor

➣ Time Constant

➣ Discharging of a Capacitor

➣ Transient Relations during capacitor charging cycle

➣ Transient Relations during

Capacitor Discharging Cycle

➣ Charging and Discharging of a Capacitor with Initial

Charge

5.1. Capacitor

A capacitor essentially consistsof two conducting surfaces separated by a layer of an insulating medium called dielectric. The conducting sur- faces may be in the form of either circular(or rectangular) platesor be of spherical or cylindrical shape. The purposeof a capacitor is to store elec- trical energy by electrostatic stress in the dielectric (the word ‘condenser’ is a misnomer since a capacitordoes not ‘condense’ electricity as such, it merely stores it).

A parallel-plate capacitor is shown in Fig. 5.1. One plate is joined to the positive end of the supplyand the otherto the negativeend or is earthed. It is experimentally found that in the presence of an earthedplate B, plate A is capableof withholding more charge than when B isnot there. When such a capacitor is put across a battery, there is a momentary flow of electrons from A to B. As negatively-charged electrons are withdrawn from A, it becomes positiveand as these electrons collecton B, it becomes negative. Hence, a p.d. is established between plates A andB. The transient flow of electronsgives rise to chargingcurrent. The strengthof the charging

Fig. 5.1

current is maximum when the two plates are uncharged but it then decreases and finally ceases when

p.d. across the plates becomes slowly and slowly equal and opposite to the battery e.m.f.

5.2.
Capacitance

The property of a capacitor to ‘store electricity’ may be called its capacitance.

As we may measure the capacity of a tank, not by the total mass or volume of water it can hold, but by the mass in kg of water required to raise its level by one metre, similarly, the capacitance of a capacitor is defined as “the amount of charge required to create a unit p.d. between its plates.”

Suppose we give Q coulomb of charge to one of the two plate of capacitor and if a p.d. of V volts is established betweenthe two, then its capacitance is

Hence, capacitance is the charge required per unit potential difference.

By definition, the unit of capacitance is coulomb/volt which is also called farad (in honour of Michael Faraday)

\ 1 farad = 1 coulomb/volt

One farad is defined as the capacitance of a capacitorwhich requires a charge of one coulomb to establish a p.d. of one volt between its plates.

One farad is actually too large for practical purposes.Hence, much smallerunits like microfarad (mF), nanofarad (nF) and micro-microfarad (mmF) or picofarad (pF) are generally employed.

1 mF = 10-9 F; 1 nF = 10-9 F ; 1 mmF or pF = 10-12F Incidentally, capacitance is that propertyof a capacitor which delays and change of voltage across it.