Download Electric Current

Electric Current
• An electric current is a flow of charge.
• The electric current in a wire is defined as
the net amount of charge that passes
through it per unit time at any point.
q
I
t
•Electric current is
measured in ampere, A.
•Where 1 A = 1 C s-1.
Conventional Current
• The direction of a Conventional current is the
direction along which imaginary positive
charge carriers may be imagined to flow.
• In a wire, electrons are the only charged
particles moving in an electrical current.
• At the right, negative
charges moving to the left
is equivalent to positive
charges moving to the
right.
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)
• When an electric field exists in the wire, the
electrons feel a force and begin to accelerate
and gain kinetic energy.
• On colliding inelastically with lattice ions,the
motion is repeated very rapidly at short time
intervals.
• The electrons soon
reach a steady
speed known as
their drift speed.
• The macroscopic
effect is a steady
current flow.
The Mechanism of current flow (2)
• Microscopically electric field energy is
converted initially to the mechanical kinetic
energy of the drifting electrons, and then to
the kinetic energy and potential energy of the
vibrating lattice ions.
• Macroscopically the internal energy of the
metal increases resulting in a temperature
rise.
Drift Speed (1)
• The diagram below shows part of a wire of crosssectional area A.
• The current in the wire is I.
• There are n free electrons per m3 of the wire.
• The charge on each electron is e.
• The electrons move with a drift speed of v.
• It can be shown that
I = nAve
v
Drift Speed (2)
• The drift speed is normally (~10-4 m s-1)
very much smaller than the electrons
average random speed (~106 m s-1).
• For example, the drift speed through a
copper wire of cross-sectional area 3.00
x 10-6 m2, with a current of 10 A will be
approximately 2.5 x 10-4 m/s.
Free Electron Number Density
• The table below shows some typical
values for n.
Type of material
Number of free
electrons per m3 (n)
Conductor
~1  1029
Semiconductor
~1  1019
Insulator
~1  109
Speed of Electric Signal
• The speed of the electric signal is the speed
of light. This means that, at the speed of
light, the removal of one electron from one
end of a long wire would affect electrons
elsewhere.
• If you think of a copper wire as a pipe
completely filled with water, then forcing a
drop of water in one end will result in a drop
at the other end being pushed out very
quickly. This is analogous to initiating an
electric field in a conductor.
Electromotive Force (e.m.f.)
• The e.m.f. of an electric source is defined
as the energy (chemical, mechanical or
light, etc.) converted into electrical energy
when unit charge passes through it.
• Unit : volts (V)
• The e.m.f. equals the potential difference
across the terminals of an electric source
on open circuit.
Potential Difference
• The potential difference across two
points in a circuit is defined as the
energy converted from electrical energy
to other forms of energy per unit charge
passing between the points outside the
source.
• V = IR
Internal Resistance
• The resistance within a source of electric
current such as a cell or generator is called
the internal resistance.
• Some of the electrical energy is wasted due
to the heating effect inside the cell.
• A real cell can be modelled as it had a
perfect emf  in series with a resistor r as
shown.

r
Measurement of Internal Resistance
• The circuit below shows an experiment to
measure the emf and internal resistance of a cell.
V

Slope = - r
V
A
I
Variation of power output with
external resistance
Po
Power output to R is a maximum
when R = r, internal resistance.
Pmax
Po 
r
 2R
(R  r )2
R
0
Variation of efficiency with the
external resistance

The efficiency equals 50 % when R = r
100 %

50 %
r
Po
R

100%
Pi
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.
Examples of Loads in an Electric Circuit
(2)
• The loading on a dynamo or battery is
generally adjusted for high efficiency.
• If a large dynamo were used with a load not
much greater than its internal resistance, the
current would be so large that the heat
generated would ruin the machine.
• With batteries and dynamos, the load
resistance is made many times greater than
the internal resistance.
Resistance in a Conductor (1)
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 m.
Resistivities of various materials
Material
Copper
Silver
Nichrome
Graphite
Germanium
Silicon
Quartz
Class
Good conductor
Good conductor
Conductor
Conductor
Semiconductor
Semiconductor
insulator
/m
1.7  10-8
1.6  10-8
1.1  10-6
8.0  10-6
0.6
2300
5.0  1016
Effect of temperature on the
resistance of a metal conductor (1)
• Heat on the atomic or molecular scale is a
direct representation of the vibration of the
atoms or molecules. Higher temperature
means more vibrations.
• When the wire is
cold the protons are
not vibrating much
so the electrons can
run between them
fairly rapidly.
Effect of temperature on the
resistance of a metal conductor (2)
• As the conductor heats up, the protons
start vibrating and moving slightly out
of position. As their motion becomes
more erratic they are more likely to get
in the way and disrupt the flow of the
electrons.
As a result, the higher
the temperature, the
higher the resistance.
R  Ro (1  T )
The variation of Current with applied
potential difference (1)
•Filament lamp
• Ohmic conductor
I
I
0
V
0
V
The variation of Current with applied
potential difference (2)
• Thermionic diode
• Thermistor
I
0
I
V
0
V
The variation of Current with applied
potential difference (3)
• Electrolyte
• Gases
I
I
0
V
0
V
The variation of Current with applied
potential difference (4)
• Semiconductor diode
I
0
V
Slide-wire potentiometer
• The potentiometer
consists of a long wire
placed on a metre rule. A
fixed potential difference
is maintained across this
wire by a cell E called the
driver cell.
Q
P
• A sliding contact is used to apply a fraction of
this potential difference across another wire PQ,
connected in parallel across AJ. The p.d. in this
wire is then known to be equal to the p.d. across
the part AJ of the potentiometer wire.
Rotary Potentiometer
• By rotating the wiper to touch the different
places on the horse-shoe, we can 'tap-off' any
fraction of the input voltage we want from
zero up to the full size of the input.
Multimeters
• A multimeter is a
moving-coil
galvanometer adapted
to measure current,
p.d. and resistance.
• A rotary switch allows
the various ranges to
be chosen.
Connections in a Multimeter (1)
• For measuring current
ranges, some internal
resistors in parallel
formed a shunt across
the meter.
• For measuring p.d.
ranges, more internal
resistors in series formed
a multiplier in series with
the meter.
Connections in a Multimeter (2)
• For measuring resistance, an internal battery
and rheostat are connected in series with the
meter and the unknown resistance.
• To measure resistance the terminals are
short-circuited and the rheostat adjusted until
the pointer gives a full deflection, i.e. is on the
zero of the ohms scale.
• The zero resistance reading will correspond
to the maximum current value.