Electric Current
• An electric current is a flow of charge.
• In metals, current is the movement of negative charge,
i.e. electrons
• In gases and electrolytes (NaCl solution), both positive
and negative charges may be involved.
Electric Current
• Current is the rate at which charge is flowing in a circuit.
It is the amount of charges that pass through any point
of the circuit per unit time.
• i.e. I = Q / t
• Current is measured in ampere, A, where 1 A = 1 C s-1.
Conventional current
• Scientist first thought that positive charges flow from the
positive terminal of a cell to the negative terminal. This is
called the conventional current direction.
• However, it was found that a current in a metal wire is in
fact a flow of negatively-charged electrons in the
opposite direction. Nevertheless, the conventional
current is still used.
+
–
electron flow
convention
current
Microscopic view of
Electric Current
• In a conducting wire, the free electrons are moving about
randomly at high speeds, (about 1/1000 of the speed of
light) bouncing off the atoms.
• Normally, the net flow of charge is zero.
The Mechanism of current flow (1)
• If a battery is connected across the ends of a conductor,
an electric field is created which causes the electrons to
accelerate and gain kinetic energy.
• Collisions occur between the accelerating electrons and
atoms of the conductor.
• As a result, the electrons lose kinetic energy and slow
down whilst the ions gain energy. This leads to a
temperature rise in the conductor. The electrons are
again accelerated and the process is repeated.
• The electrons soon reach a steady speed known as their
drift velocity.
The Mechanism of current flow
• The overall acceleration of the electrons, however, is zero
on account of their collisions. They acquire a constant
average drift velocity in the direction from the negative to
positive of the battery.
• Typically value of the average drift velocity is 10-3 m s-1.
Example 1
A hair dryer draws a current of 3 A. If it is switched on for 5
minutes,
(a)
how much charge, and
(b)
how many electrons have passed through it?
• Solution:
(a) By I = Q / t
3 = Q / (5 x 60)
Q = 900 C
(b) charge of 1 electron = 1.6 x 10-19 C
no. of electron = 900 / (1.6 x 10-19) = 5.625 x 1021
Electromotive Force (e.m.f.)
• The electromotive force or e.m.f. of a battery is the
energy transferred to unit charge from chemical
energy of the battery when the charge passes through
the battery.
• Unit : volts (V)
• The e.m.f. of a battery is 1.5 V if 1.5 J of electrical
energy is transferred to each coulomb of charge
Potential Difference
• The potential difference, p.d. or voltage across two
points in a circuit is the amount of electrical energy
which changes into other forms of energy when unit
positive charge passes between these points.
• The p.d. across two points in a circuit is 1 V if 1 J of
electrical energy is changed into other forms of energy
when 1 coulomb of charge passes between these points.
electricalenergy
p.d . 
charge
1 V = 1 J C-1.
or V  W
Q
e.m.f. 4 V
current
4 J of energy given
to each coulomb of
charge
1 J of energy changed
into heat and heat and
light energy by each
coulomb of charge
p.d. 1 V
3 J of energy
changed into heat
and heat and light
energy by each
coulomb of charge
p.d. 3 V
Potential at a point
• If a convenient point in the circuit is selected as having
zero potential, the potentials of all other points can be
stated with reference to it.
• If current flows from a point A to a point B, then A is
regarded as being at a higher potential than
• Consider the following circuit
6V
p.d. across AB
A
C
VAB = (1)(4) = 4 V
p.d. across BC
VBC = (1)(2) = 2 V
4W
B
2W
If VC = 0, VB = 2 V and VA = 6 V
If VA = 0, VB = -4 V and VC = -6 V
Internal resistance
• A high-resistance voltmeter connected across a cell on
open circuit records its e.m.f. E.
• If the cell is now connected to an external circuit in the
form of a resistor R the voltmeter reading V falls. V is
called the terminal p.d. or terminal voltage of the cell.
voltage = 3 V
voltage = 2.8 V < 3 V
V

V



closed
• In our example, the e.m.f. of the cell is 3 V and the
terminal voltage is 2.8 V. The difference between the
e.m.f. and the terminal voltage is known as the ‘lost’
volt, which is equal to 0.2 V.
• The deficiency is due to the cell itself having some
resistance.
• All power supplies, including the batteries and low
voltage power packs, have some resistance due to the
way they are made. This is called internal resistance.
‘lost’ volt v
r
e.m.f.
E
E=V+v
E = IR + Ir
I
terminal voltage V
R
For an open circuit,
I = 0 ⇒ ‘lost’ volt v = 0.
e.m.f. E = terminal voltage
V.
Example 2
Suppose a high-resistance voltmeter reads 1.5 V when
connected across a dry battery on open circuit, and 1.2 V
when the same battery is supplying a current of 0.3 A
through a lamp of. Find
(a)
the e.m.f., and
(b)
the internal resistance of the battery.
‘lost’ volt v e.m.f.
r
I
E
terminal voltage
V
R
(a)
(b)
E.m.f = 1.5 V
Lost volt = 0.3 V
0.3 = 1.2r
r = 0.25 W
Examples relating internal resistance
• The typical internal resistance of an E.H.T. is of the order
of MW (106 W)
• To limit the current it supplies and to ensure the safety
when using the E.H.T.
Variation of power output
with external resistance
‘lost’ volt e.m.f.
r
I
E
terminal voltage
2
E
R
2
Po  I R 
(R  r )2
R
I = E / (R + r)
Power output to R is a maximum
when R = r, internal resistance.
What should be the value of R such that maximum
power is delivered?
P0
r
• Hence, maximum power is
delivered (P0 is maximum) when
• R = r.
• In this case, the external resistance
is matched to the internal
resistance and the corresponding
R
power = E2/(4R)
Variation of efficiency with the external
resistance
Po
I 2R
R

 2

100%
2
Pi
I RI r Rr

100 %
When R is large,  →1
50 %
The efficiency equals 50 % when R = r
r
R
0
Examples of Loads in an Electric Circuit (1)
• Loading for greatest power output is common in
communication engineering.
• For example, the last transistor in a receiver
delivers electrical power to the loudspeaker, which
speaker converts into mechanical power as sound
waves.
• To get the loudest sound, the speaker resistance
(or impedance) is matched to the internal
resistance (or impedance) of the transistor, so that
maximum power is delivered to the speaker.
Resistance
• The resistance of a conductor is due to the collisions
between
(1) electrons and the vibrating ions (crystal lattice) and
(2) electrons and the defects in crystal lattice at very
low temperature.
• When the same p.d. is applied across different
conductors, different currents flow. Some conductors
offer more opposition or resistance to the passage of
current than others.
Resistance
• The resistance R of a conductor is defined as the ratio of
the potential difference V across it to the current I
flowing through it.
resistance
p . d . across conductor
current through conductor
V
R
I
+
•
–
•
V
A
–
Current – p.d. relationships
• Ohmic conductor
I
0
V
Their I – V graphs are straight
lines through the origin. They
obey Ohm’s law, which states
that the p.d. across a conductor
is directly proportional to the
current flowing through it,
provided that the temperature is
constant. Hence, they are called
linear or ohmic conductors.
Current – p.d. relationships
•Filament lamp
I
0
V
• The I – V graph bends over
as V and I increase,
indicating that a given
change of V causes a
smaller change in I at larger
values of V. That is, the
resistance of the tungsten
wire filament increases as
the current raises its
temperature and makes it
white-hot. In general, the
resistance of metals and
alloys increases with
temperature.
Current – p.d. relationships
• Semiconductor diode
I
0
V
The I – V graph shows that
current passes when the p.d. is
applied in one direction but is
almost zero when it acts in the
opposite direction. A diode
therefore has a small resistance if
the p.d. is applied one way round
but a very large resistance when
the p.d. is reversed.
This one-way property makes it
useful as a rectifier for changing
alternating current (a.c.) to direct
current (d.c.)
Current – p.d. relationships
• Thermistor
The I – V graph bends upwards.
This shows that its resistance
decreases sharply as its
temperature rises.
I
0
V
Current – p.d. relationships
• Electrolyte
I
0
V
The I – V graph shows that there is
almost no current flow until the
p.d. exceeds a certain value. The
phenomenon is due to the
existence of a back e.m.f., which
the applied p.d. must exceed
before the electrolyte conducts.
Conclusion:
I
0
V
• Ohm’s law as a special case of resistance behaviour. Most of
the electronic components are non-ohmic.
Effect of temperature on the resistance of
a metal conductor (2)
• For metals and a lot of insulators, when temperature is
raised, the lattice ions vibrate more vigorously,
increasing the frequency of collision between electrons
and the lattice. The average drift velocity is reduced and
the resistance therefore increases.
T ↑ ⇒ R↑
• For semi-conductors, when temperature is raised, greater
vibration of atoms breaks bonds, freeing more charge carries
(such as electrons) and thereby producing a marked decreased
of resistance.
• T ↑ ⇒ R↑
The resistance of a conductor depends
on its length and thickness.
It can be shown that
R1/A.
• Notice that the electrons
seem to be moving at the
same speed in each one
but there are many more
electrons in the larger
wire.
• This results in a larger
current which leads us to
say that the resistance is
less in a wire with a
larger cross sectional
area.
Resistance in a Conductor (2)
• The length of a conductor is similar to the
length of a hallway. A shorter hallway would
allow people to move through at a higher rate
than a longer one.
• So a shorter conductor would allow electrons
to move through at a higher rate than a longer
one too.
• It can be shown that R  l .
Resistivity of a material
1
As R 
A
and R  

We get R 
A

Hence R  
A
 is called the resistivity of the material.
The unit of  is Wm.
Resistivities of various
materials
Material
Copper
Silver
Nichrome
Graphite
Germanium
Silicon
Quartz
Class
Good conductor
Good conductor
Conductor
Conductor
Semiconductor
Semiconductor
insulator
/Wm
1.7  10-8
1.6  10-8
1.1  10-6
8.0  10-6
0.6
2300
5.0  1016
Example 3
Find the resistance of a copper wire if its length and
diameter are 5 m and 2 mm respectively.
Solution:
R = l/A
For the copper wire,  = 1.7 x 10-8
l=5m
A = pr2 = p(0.002)2 = 1.2566 x 10-5 m2
R = 1.7 x 10-8 x 5 / (1.2566 x 10-5)
= 6.76 x 10-3 W
Power and heating effect
• The power of a device is the rate at which it transfers energy.
2
W
V
P
 IV  I 2 R 
t
R