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.

• 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.

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• 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

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

e = emfVT = terminal voltage

I = currentr = internal resistanceR = total external

resistance

Terminal Voltage, emf and Internal Resistance

So that IR = e – Ir or e = IR + Irand finally e = I(R+r)

The external resistance of the circuit therefore only sees the terminal voltage and not the emf.

VT = IR

Series CircuitsIn 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 CircuitsIn 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 Series

• In Parallel

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.

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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 photo-

conductive 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: