| Contents for this page | Related topics |  |
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Electric currents produce heat in conductors Electric power The definition of emf (electromagnetic force) The emf of a battery Internal resistance Power in AC circuits Efficiency Fuses Light bulbs Additional questions |
Inductive circuits Electric machines Alternating currents Resistive, capacitive and inductive AC circuits Alternating currents and safety |
 Data Glossary |
| Learning Outcomes | ||
| After studying this section, you will (a) know about the heating effect of an electric current and the power dissipated by a current and (b) be able to solve numerical problems involving electric power. | ||
When a charge moves in a conductor, work is done by that charge. Devices can be made which convert this work into heat ( electric heaters), light (light bulbs and neon tubes), or motion, i.e. kinetic energy (power tools).
From the definition of potential difference, V, we have V = W/Q, where W is the work done by charge Q. Hence, W = VQ.
Current is the flow of charge, so that in time t, the amount of charge moving through the conductor will be Q = It.
Therefore, W = VIt gives the work done in time t, by a current I, flowing through a conductor across which the potential difference is V. This may be written in two other ways by substituting from Ohm's Law:
where R is the resistance of the conductor.
Remember that power is defined as the rate at which work is done:
By substituting from W = VIt, we obtain the formula for the power dissipated in an electric circuit, as follows:
This formula gives the power which is dissipated when a current I moves through a conductor across which there is a potential difference V.
From Ohm's law we may also write
The unit of power is the WATT, W which is equivalent to one joule per second, J.s-1.
In a circuit in which a current is present, the total rate at which energy is drawn from the source of current and dissipated in the circuit per unit current is defined as the electromotive force, (emf), in the circuit.
The emf is represented by the symbol E. From the above definition,
where P is the power dissipated in the circuit and I is the current flowing in the circuit.
The potential difference is defined as
"The potential difference between two points on a conductor is the work done per unit charge by a charge moving from a point of higher potential to that of lower potential."
Observe that potential difference is defined in terms of work and charge, whereas emf is defined in terms of power and current.
From the definition, we could define the unit of emf as the watt per ampere, which is the volt.
Both emf and potential difference have units of volts, as both are ultimately concerned with energy transformation per unit charge.
The emf of a battery may be measured by connecting a voltmeter across its terminals. This measured potential difference is the same as the emf of the battery when it is not connected to a circuit.
In general, however, when the battery is connected to a circuit the potential difference measured by the voltmeter will be lower than the emf because of the internal resistance of the battery. Some of the energy dissipated in the circuit will be dissipated in this internal resistance.
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The equivalent circuit is shown on the left, where r is the internal resistance of the battery with emf E, connected to a circuit with resistance R. The voltmeter measures the potential difference across R and not the emf of the battery which is equivalent to the potential difference across (R + r). |
Sources of electric currents, such as batteries or generators, are made of conductors. Since all conductors do have some resistance, batteries and generators will have a resistance of their own, called INTERNAL RESISTANCE, to distinguish it from the loads in a circuit, which are called EXTERNAL RESISTANCE. The internal resistance comes into play when a current is flowing through the source, and results in a DECREASE in the measured potential difference across the source terminals. If one places a voltmeter across the terminals of a battery which is part of an open circuit, the voltage that is read is the electromotive force of the battery. How does one measure the internal resistance?
In a closed circuit, the voltmeter reading across the battery terminals is less than the battery emf. The difference is the voltage drop across the internal resistance r. If we know the current that is flowing through the circuit, let us say I, then
We see that the circuit voltage, V, is inversely proportional to the circuit current, I .
Electricity is supplied as an alternating current (A.C.) for domestic and industrial use. The voltage of alternating current is not constant, as in the case of direct current current, (D.C.), and varies sinusoidally with time, at 50 cycles per second (in South Africa).
The alternating potential causes the current in the conductor to change in accordance with Ohm's law. Since the current varies continuously, how is it possible to calculate the heating effect? This can be done by defining effective values of the current, I, and the voltage, V.
"An alternating current is said to have an effective value of 1 ampere when it will develop the same amount of heat in a given resistance as would be produced by a direct current 1 ampere in the same resistance in the same time."
An effective value of the voltage can be defined in an analogous way.
If the effective values of the voltage and current are used, the power dissipation in an A.C. circuit may be calculated in the same way as for direct currents. The effective values are simply the root mean square values of the voltage and current.
In South Africa the effective value of the voltage is quoted as 220V.
Domestic appliances convert electrical energy into other forms of energy. Appliances are generally marked with the recommended operating voltage and their total power consumption at that voltage.
In the case of appliances that produce light and motion, not all the electrical energy is converted into the desired form of energy, as some of the electrical energy is converted to heat. The fraction of energy converted to the desired form is the efficiency of the appliance, e, given by
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When a current is passed through a conductor, heat is generated, This is the principle which operates in FUSES. In order to protect equipment or appliances from large, unexpected currents, a fuse (one design is shown on the left) is placed in series in the circuit. It consists of a metal wire designed to melt, and hence break the circuit, once the current through it reaches a stated value. |
| A light bulb consists of an evacuated glass container, with conducting supports to hold a coil of fine tungsten wire. As the current passes through the filament, it reaches very high temperatures and emits energy in the form of light. Tungsten is chosen as the metal for the filament as it has a high melting point (3410 ºC). The filament is in a vacuum in order to prevent oxidation of the metal, which would simply burn at the high operating temperature, if air were to be present in the bulb. |
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