Topic 5.2 Electric Circuits
3 hours
Electromotive Force
• We define the electromotive force (emf or e)
as the work per unit charge made available by
an electrical source.
W
e
q
• In the previous section, potential difference
was defined in terms of the amount of work
that has to be done per unit charge to move a
positively-charged body in an electric field.
W
V
q
e
DV
V
?
• The terms emf, potential difference and voltage
are commonly interchanged in talking about
electricity. The term electromotive force should
not be used as it is not a force at all but rather a
potential energy difference.
• For the moment, let us say that emf is the energy
supplied per unit charge, and potential difference
is the energy released (dissipated) per unit
charge.
Sources of emf are:
• electromagnetic: when a coil of wire is rotated in a
magnetic field, an induced current is produced. Power
stations use generators to produce a current.
• chemical: oxidation-reduction reactions transfer electrons
between chemicals. Dry cells, fuel cells and batteries are
examples.
• photoelectric effect: electrons are emitted from certain
metal surfaces when high frequency light is shone on their
surfaces. These photocells are used in watches, clocks,
automatic doors.
• piezoelectric effect: certain crystals can produce a charge
on one side when placed under stress. If one side of the
crystal is charged and the other not, a potential difference
exists across the crystal. This is used in crystal microphones.
• thermoelectric effect: when two pieces of certain metals
are wound together and one end is heated while the other
end is cooled, a current is produced. Thermocouples can be
used as temperature measuring devices.
Terminal Voltage, emf and Internal Resistance
e = emf
VT = terminal voltage
I = current
r = internal resistance
R = total external
resistance
The terminal voltage of a non-ideal cell is equal to its emf
minus the potential drop caused by its own internal
resistance.
VT = e - Ir
Terminal Voltage, emf and Internal Resistance
The external
resistance of the
circuit therefore only
sees the terminal
voltage and not the
emf.
VT = IR
So that
and finally
IR = e – Ir
or
e = I(R+r)
e = IR + Ir
Series Circuits
In a series circuit:
• All the components have only one current pathway.
• All components have the same current through them.
• The sum of the potential drop across each
component is equal to the emf of the cell.
Parallel Circuits
In a parallel circuit there is more than one current pathway.
• All components have the same potential difference across
them.
• The sum of the currents flowing into any point is equal to
the sum of the currents flowing out at that point.
Resistors in Series and Parallel
Real Resistors
• In Parallel
• In Series
Example: Find the equivalent resistance of
the circuit as well as the current and
voltage drops for each resistor.
Galvanometers
• Galvanometers are used to detect
electric currents. They use a property
of electromagnetism – a coil with a
current flowing in it experiences a
force when placed in a magnetic field.
Most non-digital ammeters and
voltmeters consist of a moving coil
galvanometer connected to resistors.
• Digital Multimeters (DMMs) are
becoming more common, and the
digital multimeter can act as an
ammeter, a voltmeter or an ohmmeter.
Voltmeters
A voltmeter
• is always connected across a device (in parallel).
• has a very high resistance so that it takes very
little current from the device whose potential
difference is being measured.
• has a high resistor (a multiplier) connected in
series with a galvanometer.
• an ideal voltmeter would have infinite resistance
with no current passing through it and no energy
would be dissipated in it.
Ammeters
An ammeter
• is always connected in series with a circuit.
• has a very low resistance compared with the
resistance of the circuit so that it will not alter the
current flowing in the circuit.
• has a low resistor (a shunt) connected in parallel
with a galvanometer.
• would ideally have no resistance with no
potential difference across it and no energy
would be dissipated in it.
The Potential Divider
• In electronic systems, it is often
necessary to obtain smaller
voltages from larger voltages for
the various electronic circuits. a
potential divider is a device that
produces the required voltage for
a component from a larger
voltage.
• It consists of a series of resistors
or a rheostat (variable resistor)
connected in series in a circuit. A
simple voltage divider is shown
below.
V  I ( R1  R2 )
and
V1  IR1
therefore
V1
IR1
R1


V I ( R1  R2 ) R1  R2
 R1 

V1  V 
 R1  R2 
Sensors in the Potential Divider Circuit
• A number of sensors (input transducers) that
rely on a change in resistance can be used in
conjunction with potential dividers to allow for
the transfer of energy from one form to
another. Three such sensors are:
• the light dependant resistor (LDR)
• the negative temperature coefficient thermistor
(NTC)
• strain gauges.
Light Dependent Resistors
• A light dependent resistor (LDR) is a photoconductive cell whose resistance changes with
the intensity of the incident light. Typically, it
contains a grid of interlocking electrodes made of
gold deposited on glass over which is deposited a
layer of the semiconductor, cadmium sulfide.
• Its range of resistance is from over 10 MΩ in the
dark to about 100 Ω in sunlight. A simple LDR and
its circuit symbol are shown below.
Light Dependent Resistors
• Light dependant resistors have many uses in
electronic circuits including smoke detectors,
burglar alarms, camera light meters, camera
aperture controls in automatic cameras and
controls for switching street lights off and on.
A LDR in a Potential Divider: Two Ways
Thermistors (Thermal Resistors)
• Resistors that change resistance with temperature are
called thermistors .
• They are made from ceramic materials containing a
semiconductor the main types being bead and rod
thermistors. The NTC (negative temperature coefficient)
thermistor contains a mixture of iron, nickel and cobalt
oxides with small amounts of other substances. They may
have a positive (PTC) or negative (NTC) temperature
coefficient according to the equation:
Rf = R0(1 + αt)
• where R0 equals the resistance at some reference
temperature say 0 °C, Rf is the resistance at some
temperature, t °C, above the reference temperature, and α
is the temperature coefficient for the material being used.
Thermistor Temperature Curves
PTC Thermistor
NTC Thermistor
An electronic thermometer can be
made using an NTC thermistor.
An Electrical Strain Guage
• When a metal conducting wire is put under
vertical strain, it will become longer and
thinner and as a result its resistance will
increase. An electrical strain gauge is a device
that employs this principle. It can be used to
obtain information about the size and
distribution of strains in structures such as
metal bridges and aircraft to name but two.
An Electrical Strain Guage
• A simple gauge consists of very
fine parallel threads of a
continuous metal alloy wire
cemented to a thin piece of
paper that are hooked up to a
resistance measuring device
with thick connecting wires as
shown to the right.
• When it is securely attached on
the metal to be tested, it will
experience the same strain as
the test metal and as this
happens the strain gauge wire
become longer and thinner and
as such the resistance increases.
Example: