Engineering Science EAB_S_127

Electricity Chapter 4

Introduction Capacitance Energy stored in a capacitor Charging and Discharging through a resistor Time constants

Capacitance Capacitors are devices which store electrical

charge A capacitor consists of two plates separated

by an insulator, as shown in Figure 4.1 The negative plate is connected to a low

potential and the positive plate to a high potential

Figure 4.1

Q

V

+

+

+-

-

-

Positive plateNegative plate

Insulator

Capacitance continued The total amount of the charge stored, is

denoted by Q and the voltage across the plates by V

The capacitance then is defined as Where C is in Farads 1 Farad = 1 Coulomb per Volt

Figure 4.1

Q

V

+

+

+-

-

-

Positive plateNegative plate

Insulator

][FV

QC

Energy Stored in a Capacitor When charged, a capacitor stores electrical energy Recall the formula for electrical energy in a circuit,

which is W = VQ However, we need to be careful as the voltage

between the plates in a capacitor varies from 0 to V

Hence, to be more accurate we should use the average voltage

So and we know

Hence

22

0 ababm

VVV

QV

QVW abm 2

abCVQ

2

2

1

2 ababab CVCVV

W

Energy Stored in a Capacitor: Example Question: A capacitor is supplied with 10 V in

a circuit. If its capacitance is 150µF, what is the electrical energy stored in the capacitor?

Answer:

mJJCVW ab 5.7107510101502

1

2

1 4262

Charging and Discharging a Capacitor Charging and discharging a capacitor from a DC

(direct current) source is shown below

We assume that the voltage source, V, has no internal resistance

If the switch was held in position 2 for a long time, then the capacitor would be completely discharged, Vc = 0V

V

Charging a Capacitor If the switch is then moved to position 1,

current will start to flow through the resistor R, thereby charging the capacitor, C

The voltage across the plates of the capacitor will rise in time, until after a long time, the capacitor will have the same voltage as the supply, V

V VC

Discharging a Capacitor If the switch is then moved back to position 2,

current will start to flow through the resistor R, thereby discharging the capacitor, C

The voltage across the plates of the capacitor will fall in time, until after a long time, the capacitor will have no charge at all and again, Vc = 0V

V VC

Time Constant of an RC Circuit It can be shown mathematically, that the time

for the voltage to fall to 37% of its original voltage, t = RC

The charging and discharging curves have an exponential nature

When discharging

When charging VC

VC

RC Time Constant: Example Question: If R = 1000W and C = 0.1mF, what is

the time constant of the circuit? Answer: t = RC = 1000x0.1x10-6 = 0.1 x10-3 =

100ms Hence, when discharging, the following

equation can be used to calculate the voltage

When charging

Summary Learning Outcomes:

Capacitors and capacitance Energy stored in a capacitor Charging a capacitor Time constants Exponential charging and discharging curves