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Current and Electricity Current and Charge Current is the rate of a directed flow of charge carriers. In a metallic conductor. Current is due to a directed flow of mobile (i.e. Free) electrons. The direction of conventional current is that in which positive charge carriers would move (if they could) and this is opposite to the direction in which the negative charge carriers (such as electrons) would move. The S.I. unit of electric current is the ampere and this is defined in terms of forces exerted between two straight, parallel, current- carrying conductors- in fact, this is the current flowing in each such conductor if they are 1 meter apart and exert equal and opposite forces of magnitude 1N on one another. The unit of electric charge is the coloumb (C) and this si defined as one ampere second (since quantity of charge Q = current, I x t) or as the quantity of charge flowing past a given point in one second when a steady current of one ampere is flowing. D.C. and A.C. Current exists as direct current, d.c. and as alternating current a.c. D.C represents a flow of current in one direction or sense only over time while a.c. represents a flow of current in two opposite directions or senses over time, i.e. flow and reversal of flow continuously. 2
Consider examples of current (I) / Voltage (V) time (t) graphs representing d.c. and a.c. d.c. On one side of the time axis a.c. on both side of the time axis Square wave or pulse d.c 3
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AC current 5
Rectified waveforms Once the variation is either completely above or completely below the time axis, it is d.c. Once the variation is both above and below the time axis, it is a.c. Consider sinusoidal a.c. The period T is the time taken to complete one cycle. The frequency, f, is the number of cycles per second. Note: T = 1/f and f = 1/T The peak value or amplitude is the maximum value (of V or I) in either direction. 6
Typical effects of an electric current include: 1) Heating effects 2) Magnetic effects 3) Chemical effects Quantities, units, symbols and instruments of measurements. Quantity Typical Symbol q or c Unit & Typical Symbol Coulomb - C Instrument of Measurement 1) Unit Charge 2) Number of N Charge carriers 3) Total Q Coulomb C Quantity of charge 4) Time t Second - s Watch or clock 5) Current I Ampere- A Ammeter (or galvanometer) 6) Voltage or Potential Difference 7) Electromotive force (e.m.f) V Volt - V Voltmeter E or ε Volt- V Voltmeter 8) Resistance R Ohm- Ω Ohmmeter 9) Energy E Joule- J (kwh) Joule meter 10) Work Joule- J Joule meter 11) Power P Watt- W Comments 7
Equations 1) Q = nq (where q = e and e = 1.6 x 10-19 C) 2) Q = IT 3) R = V/I 4) V = IR 5) I = V/R 6) W = QV (where W is work is also electrical energy) 7) P = IV 8) P = I 2 R 9) P = V 2 /R 10) E = Pt 11) E = V 2 t/r 1 kwh = 1000W x 3600s = 3,600,000 J Circuits and Circuit components and their symbols 8
Another common component is a potentiometer or potential divider it is an arrangement for tapping off a variable or fixed fraction of a fixed applied voltage. Certain rheostats can be arranged to operate as potential dividers; Potential Difference (p.d.) /Voltage In order for current to flow through a component there must exist a potential difference (i.e. p.d) or voltage across the component. The p.d. / voltage between or across the ends of a conductor or component is the electrical energy per unit charge converted to other forms of energy, i.e. V = E/Q => E = VQ The unit of p.d. is the volt and it is defined as one joule per coulomb. The maximum voltage that can be obtained between the terminals of an electrical power supply, such as a cell, is called the electromotive force (i.e. supply) of the power supply. 9
Resistance All components in a circuit offer electrical resistance to the flow of current- some more than others. Certain components offer very low resistances and examples of these are connecting wires, switches, power supplies and ammeters. Other components offer much higher resistances and examples of these are voltmeters and resistors (fixed and variable). The resistance of a component such as a resistor in the form of a wire depends directly on its length and inversely on its area of cross- section. Also, the resistance depends on the nature of the material of which it is made- for instance, materials such as silver, gold, copper and aluminum have low resistances. So the longer the specimen of a given material the greater its resistance and the thinner the specimen, the greater its resistance. The reverse of both of these ideas is also true. The resistance R, of a component can be determined from the equation R = V/I, where v is the p.d./voltage applied across the component and I is the current flowing through the component. The unit of resistance is the ohm (Ω). Resistors in Series and Parallel 10
Note the following 1) I = I1 = I2 = I3, i.e. the same current flows through components in series. 2) V = V1 + V2 + V3 i.e. the total individual p.d. across components in series is the sum of the individual p.d.s. 3) R = R1 + R2 + R3, i.e. the total resistance of components in series is the sum of the individual resistances. 4) I = I1 + I2 + I3, i.e. the total current through components in parallel is the sum of the individual currents. 5) V = V1 = V2 = V3, i.e. the total p.d. across components in parallel is the same as that across individual components. 11
Ammeters and Voltmeters An ammeter is an instrument for measuring the current through a component and so it must be connected in series with the component. In fact, an ammeter measures and indicates the current flowing through itself and it is assumed that the same current flows through the component since it is in series with the ammeter. 12
It is essential that the resistance of the ammeter itself be very small compared with their resistance in the circuit- otherwise inserting it into the circuit will change the very current it is to measure. An ideal ammeter has an extremely low (close to zero) resistance and hence an extremely low (close to zero) p.d. across itself. A voltmeter is an instrument used to measure p.d. (i.e. voltage) across a component and so it is connected in parallel with the component. in fact, a voltmeter measures and indicated the p.d. across itself and it is assumed that this is the same p.d. across the component since it is in parallel with the voltmeter. It is essential that the resistance of the voltmeter be very large compared with any other resistance in the circuit ( especially the resistance of the component across which it is connected) otherwise it will itself alter the very p.d. it is to measure by drawing a significant current away from the component. So an ideal voltmeter has an infinite (i.e. extremely high) resistance and hence draws a negligible (almost zero) current. 13
Ohm`s Law This law states that the p.d. applied across a metallic conductor is directly proportional to the current through the conductor, provided that physical conditions such as strain, temperature and illumination, remain constant, so V I and V/I = a constant, i.e. the resistance, R, of the metallic conductor. For a metallic conductor at constant temperature there is a linear relationship between V and I and a graph of V against I, or I against V, (known as the V- I or I- V characteristic), is a straight line through the origin (0,0). Conductors with such V- I or I- V, graphs are known as ohmic conductors. The slope of a V- I graph gives the resistance, R, of the conductor and that of a I- V graph give the reciprocal of the resistance, 1/R, of the conductor. Conductors, which do not have V- I or I- V graphs that are straight lines through the origin are called non- ohmic conductors. Consider typical I- V characteristics for both ohmic and non- ohmic conductors; Ohmic Conductors 1) Metallic conductors (such as pure metals and alloys at constant temperature) 2) An aqueous solution of copper sulphate with copper electrodes 14
Non- Ohmic conductors 1) Filament lamp/bulb 2) Carbon resistors 3) Semiconductor Diode 15
Consider a typical circuit for investigating Ohm`s law and deriving a conductor V- I or I- V characteristic: House Circuits Within the house, the connecting cables (themselves insulated- usually with white plastic) contain three insulated wires- one of these is the live wire, L, (covered with brown plastic insulation), another is the neutral wire, N, (covered with blue plastic insulation), and the third is the earth or ground wire, (covered with green/yellow plastic insulation), which is earthed (i.e. grounded) at the house 16
There are three single cables from the pole to the house two live and one neutral. Each live cables carries 110 V (r.m.s) a.c. and by using both 220V (r.m.s) a.c. can also be obtained. Most appliances require 110 V (r.m.s) a.c. and the two live 110 V (r.m.s) a.c. wires share the distribution of energy to these appliances. Certain appliances however, such as some electric stoves, some dryers and air conditioners require 220V (r.ms.) a.c. and for these, thicker connecting wires and special sockets (with matching plugs) must be used. With the house, a ring main circuit exists with the live and neutral wires running in two complete rings around the house. Circuits are tapped off from these rings such that all circuits tapped off are in parallel of each other and with the main supply. So each circuit/appliance operates at the mains voltage. The earth wire is a safety device to prevent an electrical shock to a person in the event of this person touching the metal case or housing of an appliance, which has made contact with a live wire. The earth wire provides a safe alternative path (rather than through the person`s body) for the current to the earth. In addition, the large current (due to the small resistance), which flows in the earth wire, may cause the fuse (in the L wire- E wire circuit) to blow and so break the circuit and turn of the current- thus rendering that circuit safe. A fuse or a circuit breaker is a safety device to minimize a possibility of an overload (i.e. excess) of current flowing through a given 17
appliance or circuit- such an occurrence can lead to i) appliance damage ii) electrical fires. A fuse can exist as a metal strip, which melts (i.e. blows ). When a current above a particular value (i.e. the fuse rating) flows through it acts as a circuit breaker, which switches off when a current above a particular value (i.e. the breaker rating) flows through it. The former type generates on the heating effect of a current while the latter type operates on the magnetic effect of a current. The fuse or circuit breaker rating must be greater than the operating current required, but a close as possible to this operating current so that the fuse/circuit breaker will blow (i.e. melt) switch off before overloading can occur. Switches and fuses must always be placed in the live wire Advantages of the parallel connection of domestic appliance include: 1) A malfunction of one appliance does not affect the operation of other appliances. 2) Each appliance can be independently controlled 3) Each appliance can be operated at its rated power 4) All appliances operate at the same voltage- thus appliances can be standardized with respect to operating voltage. 18
Adverse effects of an incorrect or fluctuating supply to an appliance include: 1) Current surges which can cause overload and thus lead to i) damage to an appliance ii) electrical fires 2) Current/voltage underload, which can result in an appliance operating below its rated power, or even not operating at all. Ways of reducing waste electrical energy include; 1) Switching off all appliances (e.g. lights) when not in use. 2) Ensuring that all heating /cooling appliances (e.g. electrical stoves /refrigerators) are adequately insulated. 3) Operating appliances (such as air- conditioners) at their lowest possible power rating that will still achieve the objective of using the appliance. 4) Adequately insulating all buildings/rooms that use air conditioners. Electronics the diode A diode is a device with little or no resistance in one direction (i.e. forward bias) and very high resistance in the opposite direction (i.e. reverse bias). 19
A diode conducts in only one direction, i.e. when forward biased it will therefore rectify a.c. i.e. convert a.c. to d.c. the d.c. that results is referred to as half- wave rectified a.c. A typical circuit giving this output is Four diodes connected in a special circuit called a bridge rectifier can produce full wave rectified a.c. 20
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