Electric Current

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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.

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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.

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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.

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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.

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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.

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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.

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Example 1A 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

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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

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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.

1 V 1 J C-1.
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(No Transcript)
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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

p.d. across AB VAB (1)(4) 4 V p.d. across BC
VBC (1)(2) 2 V
If VC 0, VB and VA If VA 0, VB and
VC
2 V
6 V
-4 V
-6 V
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Internal resistance
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• 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.
• 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.

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• 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.

E V v E IR Ir
For an open circuit, I 0 ? lost volt v
0. e.m.f. E terminal voltage V.
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Example 2Suppose 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.
(a) E.m.f 1.5 V (b) Lost volt 0.3 V 0.3
1.2r r 0.25 W
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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.

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Variation of power output with external resistance
lost volt
e.m.f.
r E
terminal voltage
I
R
Power output to R is a maximum when R r,
internal resistance.
I E / (R r)
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What should be the value of R such that maximum
power is delivered?

• 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
  power E2/(4R)

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Variation of efficiency with the external
resistance
100
When R is large, h ?1
50
The efficiency equals 50 when R r
r
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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.

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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.

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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.

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Current p.d. relationships

• Ohmic conductor

Their I V graphs are straight lines through the
origin. They obey Ohms 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.
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Current p.d. relationships

• Filament lamp

• 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.

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Current p.d. relationships

• Semiconductor diode

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.)
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Current p.d. relationships

• Thermistor

The I V graph bends upwards. This shows that
its resistance decreases sharply as its
temperature rises.
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Current p.d. relationships

• Electrolyte

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.
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Conclusion

• Ohms law as a special case of resistance
  behaviour. Most of the electronic components are
  non-ohmic.

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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?
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• 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?

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The resistance of a conductor depends on its
length and thickness.

• 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.

It can be shown that R?1/A.
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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 .

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Resistivity of a material

• ? is called the resistivity of the material.

The unit of ? is ?m.
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Resistivities of various materials
Material Class ?/?m
Copper Good conductor 1.7 ? 10-8
Silver Good conductor 1.6 ? 10-8
Nichrome Conductor 1.1 ? 10-6
Graphite Conductor 8.0 ? 10-6
Germanium Semiconductor 0.6
Silicon Semiconductor 2300
Quartz insulator 5.0 ? 1016
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Example 3Find the resistance of a copper wire if
its length and diameter are 5 m and 2 mm
respectively.

• Solution
• R rl/A
• For the copper wire, r 1.7 x 10-8
• l 5 m
• 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

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Power and heating effect

• The power of a device is the rate at which it
  transfers energy.