Current Electricity PDF

1 Current Electricity Current Electricity Current Electromotive force Potential difference Resistance  2...

1 Current Electricity Current Electricity Current Electromotive force Potential difference Resistance  2 Current Electricity State that a current is a flow of charge and that current is measured in amperes. Current  3 Current Electricity Electric Current  Current is the rate of flow of charge, Q.  When charges flow, they can be positive or negative.  For historical reason, the direction of conventional current is taken as the direction a positive charge will flow.  4 Current Electricity  In conductor, the current is due to motion of negatively charged electrons. Therefore in a circuit, the direction of conventional current is opposite to the direction of motion of electrons.  5 Current Electricity Do calculations using the equation charge = current × time. Current  6 Current Electricity Calculating Current  Suppose that Q flows past a given point in a wire in a time t. The electric current I in the wire is Q I t  The SI unit for current is coulomb per second (Cs-1) or Ampere (A).  7 Current Electricity Problem Solving 1. A charge of 10 coulombs passes round a circuit in 4 s. Calculate the average current. 2. If 20 C of charge pass a point in a circuit in 1 s, what current is flowing? 3. A charge of 4 C passes a point in a circuit in 5 s. Calculate the current flowing through the circuit. 4. A current of 4 A flows around a circuit for 10 s. How much charge flows around the circuit in this time?  8 Current Electricity Problem Solving 5. When a starter motor of a car is switched on for 0.5 s, 16 C of charge passes through the wires in the motor. How large is the electric current? 6. A 3 A current flows in a circuit for 2 minutes. What is the total charge flowing in the circuit. 7. A charge of 120 C flows for 4 minutes. What is the current? 8. A charge of 60 C produces a current of 0.5 A. How long does this take?  9 Current Electricity Describe the use of an ammeter with different ranges. Current  10 Current Electricity Measuring Current  To measure the size of an electric current, an ammeter can be used.  11 Current Electricity  12 Current Electricity  13 Current Electricity  The ammeter is connected in series with the component.  14 Current Electricity Explain that electromotive force (e.m.f.) is measured by the energy dissipated by a source in driving a unit charge around a complete circuit. Electromotive Force  15 Current Electricity State that e.m.f. is work done/charge. Electromotive Force  16 Current Electricity State that the volt is given by J/C. Electromotive Force  17 Current Electricity Electromotive force  In a cell or battery, the chemical changes take place which provide the energy required to push the electric charge (electrons) round the circuit.  The electromotive force (e.m.f.) of any electrical source is the work done by the source in driving a unit charge around a complete circuit.  The SI unit for e.m.f. is joule per coulomb (J/C) or the volt (V).  18 Current Electricity Calculate the total e.m.f. where several sources are arranged in series and discuss how this is used in the design of batteries. Electromotive Force  19 Current Electricity Discuss the advantage of making a battery from several equal voltage sources of e.m.f. arranged in parallel. Electromotive Force  20 Current Electricity Cells in series  The connection gives an increased e.m.f. because charges gain potential energy from all three cells when they pass through the cells.  The combined e.m.f. is calculated by adding up the individual e.m.f.s. Cells in parallel Current Electricity 21  Charges flowing round the circuit will split into three equal portions when they reach A and each portion passes through one cell only.  The gain in potential energy for any charge in each portion is only from one of the three cells. The advantages of this arrangement are a. The cells will last longer before going ‘flat’ b. The cells are able to supply a higher current  22 Current Electricity Example 1. What is the combined e.m.f. of each of the following combinations of cells? a. two 2.0 V cells in series b. two 2.0 V cells in parallel c. six 2.0 V cells in series  23 Current Electricity State that the potential difference (p.d.) across a circuit component is measured in volts. Potential Difference  24 Current Electricity State that the p.d. across a component in a circuit is given by the work done in the component/charge passed through the component. Potential Difference  25 Current Electricity Potential difference  The potential difference across a component is defined as the work done to drive a unit charge through the component. W Potential difference = Work done V Charge Q  The SI unit for potential difference is joule per coulomb (J/C) or the volt (V).  26 Current Electricity Example 1. How much energy must a battery add to a charge of 35 C in a circuit to move it from a point at a potential of 60 V to another point where the potential is 83 V? 2. When 2 C of charge flows through a component in an electrical circuit, 20 J of work is done. What is the potential difference across the component 3. How much work is does it take to move a charge of 30 C through a potential difference of 6 V? 4. To toast a couple of slices bread, a toaster has to use 30 000 joules of energy, drawn from a 110 V wall outlet. How much charge flows through the toaster.  27 Current Electricity Describe the use of a voltmeter with different ranges. Potential Difference  28 Current Electricity Measuring Potential Difference  The potential difference across two points in a circuit can be measured by a voltmeter.  29 Current Electricity  30 Current Electricity 1. When there is an electric current in a metal wire, what flows through the wire? A. atoms B. electrons C. neutrons D. protons  31 Current Electricity 2. The current in an electric heater is 10 A. It is switched on for five minutes. 3. How much charge flows through the heater? A. 0.5 C B. 2C C. 50 C D. 3000 C  32 Current Electricity 3. The diagram shows a simple electric circuit.  33 Current Electricity 1. Which row describes the charge on an electron and the direction of electron flow through the resistor? A  34 Current Electricity 4. The diagram shows a battery connected to two identical resistors. Three ammeters M1, M2 and M3 are connected in the circuit.  35 Current Electricity 1. Meter M1 reads 1.0 A. 2. What are the readings on M2 and on M3? D  36 Current Electricity 5. In the circuit shown, ammeter X reads 0.5 A.  37 Current Electricity 1. What does ammeter Y read? B  38 Current Electricity 6. Two faulty ammeters and two perfect ammeters are connected in series in the circuit shown.  39 Current Electricity A. The readings on the ammeters are 1. A1 2.9 A 2. A2 3.1 A 3. A3 3.1 A 4. A4 3.3 A B. Which two ammeters are faulty? A. A1 and A2 B. A1 and A4 C. A2 and A3 D. A3 and A4  40 Current Electricity 7. The diagram shows a circuit containing two ammeters and three resistors.  41 Current Electricity 1. Which of the ammeters will show the current in resistor R 2? A. ammeter X only B. ammeter Y only C. both ammeter X and ammeter Y D. neither ammeter X nor ammeter Y  42 Current Electricity 8. What is measured by the energy dissipated when a source drives a unit charge round a complete circuit? A. electromotive force B. potential difference C. Power D. resistance  43 Current Electricity 9. A cell is connected to a resistor. 10. What is the e.m.f. of the cell equal to? A. The potential difference across the resistor for each unit of current. B. The power produced in the circuit for each unit of charge that passes. C. The work done in the circuit for each unit of charge that passes. D. The work done in the circuit for each unit of current.  44 Current Electricity 10. An electrical quantity is defined as ‘the energy converted by a source in driving a unit charge round a complete circuit.’ 11. What is this quantity called? A. current B. electromotive force C. potential difference D. power  45 Current Electricity 11. How could the unit of potential difference, the volt, also be written? A. A/s B. C/A C. C/J D. J/C  46 Current Electricity 12. One volt can also be written as A. one coulomb per ampere. B. one coulomb per joule. C. one joule per ampere. D. one joule per coulomb.  47 Current Electricity 13. The diagram shows two resistors connected in series with a cell.  48 Current Electricity 1. Which statement defines the potential difference across XY? A. the power needed to drive a unit charge through the cell B. the power needed to drive a unit charge between X and Y C. the work done in driving a unit charge through the cell D. the work done in driving a unit charge between X and Y  49 Current Electricity 14. A student wishes to measure the electromotive force (e.m.f.) of a battery and the potential difference (p.d.) across a resistor. 15. She has the resistor, the battery and some connecting wires. 16. What else does she need? A. a voltmeter only B. an ammeter only C. an ammeter and a voltmeter D. a force meter (newton meter) and a voltmeter  50 Current Electricity 15. The diagram shows a voltmeter adapted to measure a range from 0–100 mV. The voltmeter is measuring the potential difference in a circuit.  51 Current Electricity 1. What is the reading on the voltmeter? A. 0.06 mV B. 0.6 mV C. 6 mV D. 60 mV  52 Current Electricity 16. Which circuit shows how a voltmeter is connected to measure the potential difference across the cell? A  53 Current Electricity 17. The potential difference between the ends of a conductor is 12 V. 18. How much electrical energy is converted to other forms of energy in the conductor when 100 C of charge flows through it? A. 0.12 J B. 8.3 J C. 88 J D. 1200 J  54 Current Electricity State that resistance = p.d./current and use the equation resistance = voltage/current in calculations. Resistance  55 Current Electricity Resistor  A resistor is a component in an electrical circuit which provides a known value of resistance.  Its purpose is to control the size of the current flowing in a circuit. Electrical symbol for a fixed Electrical symbol for a resistor variable resistor  56 Current Electricity Resistance  Electrical resistance is a measure of the degree to which an electrical component opposes the passage of an electric current.  Resistance is defined as the ratio of the potential difference across the component to the current flowing through it. Potential difference Resistance = Current  57 Current Electricity  The unit of resistance is the ohm (Ω).  A resistor has a resistance of one ohm if a current of one ampere flows through it when the potential difference across it is one volt.  58 Current Electricity Problem Solving 1. When a current of 2 A flows through a resistor, the potential difference across the resistor is 10 V. What is the resistance of the resistor. 2. When a wire is connected to a 9 V battery, the current is 0.020 A. What is the resistance of the wire? 3. How much is the current in a light bulb whose resistance is 350 Ω when the bulb is connected to a 110 V outlet? 4. A moving-coil galvanometer has a resistance of 40 Ω and gives a full-scale deflection of 2 mA. What is the potential difference across its terminals when this current is flowing?  59 Current Electricity 5. A resistor allows a current of 0.02 A to flow through it when there is a p.d of 10.0 V between its ends. What is its resistance? 6. A 12 Ω resistor has a p.d of 6 V across it. What is the current through the resistor? 7. What p.d. is needed to make a current of 1 A flow through a 20 Ω resistor? 8. What current flow when p.d. of 14.5 V is connected across a 1000 Ω resistor?  60 Current Electricity Describe an experiment to measure the resistance of a metallic conductor using a voltmeter and an ammeter and make the necessary calculations. Resistance  61 Current Electricity  Aim: To measure electrical resistance of metallic conductor.  Apparatus:  DC Supply  Rheostat (Variable Resistor)  Voltmeter  Ammeter  62 Current Electricity  Procedure:  Arrange the apparatus as shown below  63 Current Electricity  Procedure  Adjust the variable resistor the maximum resistance to get a small current flows in the circuit.  Record the ammeter reading (I) and voltmeter reading (V).  Adjust the variable resistor to allow a large current to flow in the circuit. Record the values of I and V.  Repeat for another 5 sets of I and V.  64 Current Electricity  Graph  Plot the graph of V (V) and I (A).  Calculation  Determine the gradient of the graph  65 Current Electricity  Result  The gradient of the graph gives the resistance of the load R  66 Current Electricity Discuss the temperature limitation on Ohm’s Law. Resistance  67 Current Electricity Describe the effect of temperature increase on the resistance of a resistor and a filament lamp and draw the respective sketch graphs of current/voltage. Resistance  68 Current Electricity Ohm’s Law  For some materials, the resistance is constant.  A resistor that has constant resistance is said to obey Ohm’s law.  Ohm’s law states that current through a metal conductor is directly proportional to the potential difference across the ends of the conductor provided that the physical condition and the temperature remain constant.  69 Current Electricity IV V  constant I  70 Current Electricity Metallic Conductor  When X is a metallic conductor, the graph is a straight line passing through the origin.  The current I is directly proportional to potential difference V.  The conductor obey Ohm’s law and has a constant resistance.  71 Current Electricity Resistance Versus Temperature  The value of a resistor changes with changing temperature as the resistivity of the material is changed caused mainly by the changing activity of the atoms of that make up the resistor.  For conductors, their resistivity increase with an increase in temperature. However an insulators are able to decrease their resistivity with an increase in temperature.  72 Current Electricity  In a conductor where a large number of free electrons flowing through it, the vibration of the atoms causes many collisions between the free electrons and the captive electrons.  Each collision uses up some energy from the free electron and is the basic cause of resistance.  The more the atoms jostle around in the material the more collisions are caused and hence the greater the resistance to current flow.  73 Current Electricity  In an insulator as there are so few free electrons that hardly any current can flow.  Heating an insulating material vibrates the atoms, and if we heat it sufficiently the atoms vibrate violently enough to actually shake some of their captive electrons free, creating free electrons to become carriers of current.  Thus at high temperatures the resistance of an insulator can fall, sometimes dramatically.  74 Current Electricity Filament Lamp  As the current through the filament increases, the heating effect caused in the lamp also increases and so the temperature of the filament rises.  This increase in the filament's temperature also increases the resistance of the filament.  As a result the rate of increase of the current decreases and a greater change in the potential difference is required to cause a change in the current.  75 Current Electricity Filament Lamp  When X is a filament lamp, the graph is a curve.  Current I is not proportional to potential difference V.  V increases more than I.  It does not obey Ohm’s law and its resistance increases as the current increases  76 Current Electricity Use quantitatively the proportionality between resistance and the length and the cross-sectional area of a wire. Resistance  77 Current Electricity Factors affecting Resistance  Length – Doubling the length of a wire doubles its resistance.  Cross-sectional area – halving the ‘end on’ area of a wire doubles its resistance. So a thin wire has more resistance than a copper wire of the same size.  Material – A nichrome wire has more resistance than a copper wire of the same size.  Temperature – For metal conductors, resistance increases with temperature. For semiconductors, it decreases with temperature.  78 Current Electricity  From the experiment on resistance of metallic conductor – the resistance R of a uniform wire is directly proportional to its length l, and inversely proportional to its cross-sectional area A. 1 R l R A  79 Current Electricity  Combining both the results, we obtain l l R R A A  Where ρ is a constant known as the resistivity of the material of the wire. Ρ is a property of the material and does not depend on size or shape of the wire. The SI unit for ρ is Ωm  80 Current Electricity Material Resistivity ρ / Ω m Silver 1.6 × 10-8 Copper 1.7 × 10-8 Aluminium 2.8 × 10-8 Tungsten 5.5 × 10-8 Iron 9.8 × 10-8 Manganin 44 × 10-8 Constantan 49 × 10-8 Mercury 96 × 10-8 Nichrome 100 × 10-8 Graphite 200 × 10-8 Resistivities of some materials  81 Current Electricity Problem Solving 1. The resistivity of copper at room temperature is 1.72 х 10-6 Ωcm. What is the resistance of a copper wire 350 cm long and 0.025 cm2 in cross section. 2. We would like to make a 600 Ω resistor out of Nichrome wire with a cross-sectional area of 3.0 х 10-3 cm2. If the resistivity of Nichrome is 110 х 10-6 Ωcm, how long should the wire be? 3. A wire 0.40 m long and of diameter 0.60 m has a resistance of 1.5 Ω. What is the resistivity of the material which it is made? 4. What length of resistance wire of diameter 0.06 m and resistivity 1.1× 10-6 Ωm, would you cut from a reel in order to make a 44 Ω resistor? 5. A 1.0 m length of wire is found to have a resistance of 40 Ω. What would be the resistance of a piece of the same wire of length 2.0 m?  82 Current Electricity Calculate the net effect of a number of resistors in series and in parallel. Resistance  83 Current Electricity Resistors in Series  If two (or more) resistors are connected in series, the give higher resistance than any of the resistors by itself. .  84 Current Electricity  For resistors in series, the effective resistance is the sum of the individual resistances R  R1  R2  R3  85 Current Electricity Resistors in Parallel  If two (or more) resistors are connected in parallel, they give a lower resistance than any of the resistors by itself.  86. Current Electricity  For resistors in parallel, the reciprocal of the effective resistance is equal to the sum of the reciprocals of individual resistances. 1 1 1 1    R R1 R2 R3  87 Current Electricity  For two resistors in parallel, the formula can be rearranged as R1  R2 R R1  R2  88 Current Electricity Problem Solving 1. Find the total resistance for each of the following resistor arrangement (a) (b) 10  25  6 6 6 (c) 10  (d) 25  6 6 6  89 Current Electricity (e) (f) 10  6 25  6 10  6  90 Current Electricity Problem Solving 2. Determine the total effective resistance between point X and Y. (a) 5  5 (b) 5 5 8 X Y 5 5 15  X Y  91 Current Electricity Describe the operation of a light-dependent resistor. Resistance  92 Current Electricity LDR  LDRs (light-dependent resistors) are used to detect light levels, for example, in automatic security lights. Their resistance decreases as the light intensity increases:  In the dark and at low light levels, the resistance of an LDR is high, and little current can flow through it.  In bright light, the resistance of an LDR is low, and more current can flow through it.  93 Current Electricity  LDRs are also useful for controlling how long the shutter should remain open on a digital camera.  94 Current Electricity 1. A pupil measures the potential difference across a device and the current in it. 2. Which calculation gives the resistance of the device? A. current + potential difference B. current ÷ potential difference C. potential difference ÷ current D. potential difference × current  95 Current Electricity 2. What are the symbols used for the units of current and resistance? B  96 Current Electricity 3. A circuit is set up to measure the resistance of a resistor R. The meter readings are 2.0 A and 3.0 V.  97 Current Electricity 1. What is the resistance of the resistor R? A. 0.67 Ω B. 1.5 Ω C. 5.0 Ω D. 6.0 Ω  98 Current Electricity 4. The circuit shows a current I in a resistor of resistance R.  99 Current Electricity 1. Which line gives possible values of I and of R? B  100 Current Electricity 5. The table shows the voltage and current ratings for four electric heaters. 6. Which heater has the least resistance? B  101 Current Electricity 6. A potential difference (p.d.) across a resistor causes a current in it.  102 Current Electricity 1. The p.d. and the resistance of the resistor can both be changed. 2. Which row shows two changes that will both increase the current in the resistor? C  103 Current Electricity 7. Ohm’s law states that the current in a conductor is proportional to the potential difference across it, provided that a certain quantity remains constant. 8. What is this quantity? A. length B. pressure C. temperature D. thickness  104 Current Electricity 8. The diagram shows the current I / voltage V graph for a length of resistance wire.  105 Current Electricity 1. Where can Ohm’s law be applied to the wire? A. at Y only B. at Z only C. from X to Y D. from X to Z  106 Current Electricity 9. Which graph shows how the current changes when the voltage across a fixed resistance is varied? A  107 Current Electricity 10. When a filament lamp is switched on, there is a current in the lamp. As the temperature of the filament rises, its resistance changes. 11. Which pair of graphs shows how the resistance R of the filament and the current I vary with time after the lamp is switched on?  108 Current Electricity B  109 Current Electricity 11. The circuit diagram shows three resistors in parallel with a battery.  110 Current Electricity 1. What is the effective resistance of these three resistors? A. 0.57 Ω B. 0.86 Ω C. 1.75 Ω D. 7.00 Ω  111 Current Electricity 12. When three identical resistors are connected in series, their combined resistance is 6 Ω.  112 Current Electricity 1. What is their combined resistance when they are connected in parallel? B  113 Current Electricity 13. In the circuits shown, all the resistors are identical. 14. Which circuit has the least resistance? C  114 Current Electricity 14. A length of resistance wire is used as a resistor in a simple circuit.  115 Current Electricity 1. Four separate changes are made to the wire. 2. Which change will not reduce the value of the resistance of the wire? A. It is covered in an insulating sleeve. B. Its cross-sectional area is increased. C. Its length is decreased. D. Its temperature is decreased.  116 Current Electricity 15. Which factors will both increase the resistance of a wire in a circuit? D  117 Current Electricity 16. The table shows the lengths and diameters of four copper wires. 17. Which wire has the least resistance? B  118 Current Electricity 17. Four wires are made from the same material. 1. Which wire has the greatest resistance? C  119 Current Electricity 18. A wire has a resistance of 8 Ω. A second wire, made of the same material, has half the length and twice the cross- sectional area. 1. What is the resistance of the second wire? A. 1Ω B. 2Ω C. 8Ω D. 16 Ω  120 Current Electricity 19. A student uses a length of wire as a resistor. He discovers that the resistance of the wire is too small. 20. To be certain of making a resistor of higher value, he should use a piece of wire that is A. longer and thicker. B. longer and thinner. C. shorter and thicker. D. shorter and thinner.