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CHAPTER 17 Current Electricity © 2013 Marshall Cavendish International (Singapore) Private Limited Chapter 17 Current Electricity 17.1 Electric Current 17.2 Electromotive Force and Potential Difference 17.3 Resistance 17.4 Resistivity 17.1 Electric Current Learning Outcomes At the end of this section, you should be able to: • define the term current and state its SI unit; • differentiate between conventional current and electron flow; • apply the formula charge = current × time to solve problems; • draw electric circuit diagrams. Electric Current What is Electric Current? Video on Lightning & Thunder http://www.youtube.com/watch?v=Sp9bKDHRfsM Good Electrical Conductors Things that have free electrons • Metals (copper & zinc? • What’s the best conductor? • How about water? Good Insulators Things that do not allow electrons to flow • rubber 17.1 Electric Current What is Electric Current? An electric current is formed by moving charges. Electric current is a measure of the rate of flow of electrons through a conductor. Q I= t where I = current; Q = charge; t = time taken. The SI unit of electric current is the ampere (A). 17.1 Electric Current Electron Flow • Electric current is actually caused by the flow of electrons from the negative terminal to the positive terminal. 17.1 Electric Current How do We Measure Electric Current? • We make use of an ammeter to measure current. • The ammeter should be connected in series to the circuit. 17.1 Electric Current Main Components of a Circuit • A typical electric circuit consists of four main components. A source of electromotive force that drives electric charges around the circuit. Wires Conductors that connect the components together. Dry cell A load in which moving charges can do a useful job. Switch A method of opening or closing the circuit. Bulb 17.1 Electric Current Drawing Circuit Diagrams • Electric circuits can be represented by circuit diagrams. • Can you identify what the symbols in the circuit diagram below represent? ammeter bulb cell connecting wires switch 17.1 Electric Current Drawing Circuit Diagrams Some common components and their symbols are listed in the tables below. 17.1 Electric Current Interpreting Circuit Diagrams Open circuit A circuit in which current is unable to flow due to breaks in the circuit. 17.1 Electric Current Interpreting Circuit Diagrams Short circuit An alternative path of lower resistance is present and hence, current flows through wire X instead of the bulb. Chapter 17 Current Electricity 17.1 Electric Current 17.2 Electromotive Force and Potential Difference 17.3 Resistance 17.4 Resistivity 17.2 Electromotive Force and Potential Difference Learning Outcomes At the end of this section, you should be able to: • define electromotive force (e.m.f.) and potential difference (p.d); • state the SI unit of e.m.f. and p.d.; • calculate the e.m.f. when a few sources are arranged in series. 17.2 Electromotive Force and Potential Difference Recall We saw this circuit in Section 17.1. What is the role of the battery in the circuit? Why do you need a battery to make the bulb light up? 17.2 Electromotive Force and Potential Difference What is Electromotive Force? • A battery functions like a water pump. • A water pump does work (providing energy) to drive the water around the pipe. • Likewise, a battery does work to drive electrons around the circuit. 17.2 Electromotive Force and Potential Difference What is Electromotive Force? The electromotive force (e.m.f) of an electrical energy source is defined as the work done by a source in driving a unit charge around a complete circuit. W e= Q where ε = e.m.f. of electrical energy source; W = work done (amount of non-electrical energy converted to electrical energy); Q = amount of charge. SI unit of e.m.f is the joule per coulomb (J C–1) or volt (V). 17.2 Electromotive Force and Potential Difference How do We Measure E.m.f.? • We use a voltmeter to measure e.m.f. • The positive and negative terminals of a voltmeter should be connected to the positive and negative terminals respectively of the electrical source. 17.2 Electromotive Force and Potential Difference Arrangement of Cells Series arrangement When cells are arranged in series, the resultant e.m.f. is the sum of all the e.m.f.s of the cells. Parallel arrangement When cells are arranged in parallel, the resultant e.m.f. is equal to that of a single cell. 17.2 Electromotive Force and Potential Difference What is Potential Difference? The potential difference (p.d.) across a component in an electric circuit is the work done to drive a unit charge through the component. W V= Q where V = p.d. across a component; W = work done (amount of electrical energy converted to other forms); Q = amount of charge. The SI unit of potential difference is the volt (V). 17.2 Electromotive Force and Potential Difference How do We Measure P.d.? • We make use of a voltmeter to measure p.d. • The voltmeter should be connected in parallel with the component. 17.2 Electromotive Force and Potential Difference E.m.f. versus P.d. Electromotive force Associated with an electrical energy source (e.g. a dry cell) Potential difference Associated with two points in an electric circuit It is the work done by the source in driving a unit charge around a complete circuit. It is the work done to drive a unit charge through two points. 17.2 Electromotive Force and Potential Difference Question What will the voltmeter reading show? A The e.m.f. of the electrical source (the three cells in series) B The e.m.f. of the bulb C The potential difference across the bulb Chapter 17 Current Electricity 17.1 Electric Current 17.2 Electromotive Force and Potential Difference 17.3 Resistance 17.4 Resistivity 17.3 Resistance Learning Outcomes At the end of this section, you should be able to: • define the term resistance; • apply the formula resistance = to solve problems; p.d. current • describe an experiment to determine resistance; • state Ohm’s Law; • understand and draw the I−V characteristic graphs for ohmic and non-ohmic conductors; • describe the relationship between the resistance of a metallic conductor and its temperature. 17.3 Resistance Recall Earlier, we used the water pump analogy to help us understand e.m.f. obstacle Question Predict what will happen if a porous plate (an obstacle) is placed in the path of the water flow. 17.3 Resistance What is Resistance? resistor Resistor added Rate of flow of electric charges reduced Current is reduced Ammeter reading will be reduced • Resistance is the difficulty for an electric current to pass through a material. • It restricts the movement of free electrons in the material. 17.3 Resistance What is Resistance? The resistance of a component is the ratio of the potential difference across the component to the current flowing through the component. V R= I where R = resistance of a component; V = p.d. across a component; I = current flowing through component. The SI unit of resistance is the ohm (Ω). 17.3 Resistance Activity (Group) Objective Design an electric circuit that can be used to measure the resistance of a component. Instructions Resistance = p.d. current 1. In groups, design a circuit that can be used to determine the resistance of a bulb. 2. Using the materials given, check if your design works. 17.3 Resistance Circuit for Measuring Resistance Note that: • The ammeter is connected in series with the bulb. • The voltmeter is connected in parallel with the bulb. 17.3 Resistance What are Resistors? • A resistor is a conductor in a circuit that is used to control the size of the current flowing in a circuit. • There are two types of resistors — fixed resistors and variable resistors (or rheostats). 17.3 Resistance Ohm’s Law Ohm’s Law states that the current passing through a metallic conductor is directly proportional to the potential difference across it, provided that physical conditions remain constant. I µV where I = current; V = potential difference. 17.3 Resistance Ohmic and Non-ohmic Conductors • Ohmic conductors are conductors that obey Ohm’s Law. • Non-ohmic conductors are conductors that do not obey Ohm’s Law. Ohmic conductors The I−V graph of an ohmic conductor is a straight line that passes through the origin. 17.3 Resistance Non-ohmic conductors • They do not obey Ohm’s Law and their resistance R can vary. • Their I−V graphs are not straight lines, which means the ratio V/I is not a constant. Chapter 17 Current Electricity 17.1 Electric Current 17.2 Electromotive Force and Potential Difference 17.3 Resistance 17.4 Resistivity 17.4 Resistivity Learning Outcome At the end of this section, you should be able to: • apply the relationship of the proportionality of resistance to the length and cross-sectional area of a wire to solve problems. 17.4 Resistivity Recall Ohm’s Law states that the current passing through a metallic conductor is directly proportional to the potential difference across it, provided that physical conditions remain constant. Other than temperature, what physical conditions affect the resistance of a component? 17.4 Resistivity Other than temperature, the resistance R of a conductor also depends on 1. its length l; 2. its cross-sectional area A; 3. the material it is made of (i.e. resistivity ρ). conductor R= l A rl A 17.4 Resistivity Resistivity Rewriting R = r l , we can obtain the formula for resistivity. A RA r= l where ρ = resistivity of conductor; R = resistance of conductor; A = cross-sectional area of conductor; l = length of conductor. The SI unit of resistivity is the ohm metre (Ω m). 17.4 Resistivity Resistivity • Different materials have different resistivities. • Resistivity is a property of the material and it is independent of the dimensions of the material. • The lower the resistivity of a material, the better it is at conducting electricity. 17.4 Resistivity Worked Example A length of resistance wire 50 cm long is connected in series with an ammeter and a 3 V battery. The ammeter reading is 0.15 A. (a) Determine the resistance of the wire. (b) The length of the wire is doubled and its cross-sectional area halved. Determine the new resistance and hence ammeter reading. (c) Given that the diameter of the 50 cm long wire is 5 mm, determine its resistivity. 17.4 Resistivity Solution (a) R = V ÷ I = 3 ÷ 0.15 = 20 Ω (b) l Rµ A kl1 20 = - - - -(1) A1 k 2l1 - - - (2) 1 A 2 1 20 1 (1) ¸ (2) : = R2 4 R2 = (c) RA l 20 ´ p ´ 0.00252 = 0.5 = 7.85 ´ 10 -4 Wm r= R2 = 80W I= 3 = 0.0375A 80 Chapter 17 Current Electricity Electric current I (SI unit: A) I= Resistance R (SI unit: Ω) related to defined as rate of flow of Q t where where t = time (continued on next slide) Charge Q (SI unit: C) related to Electromotive force ε (SI unit: V) Potential difference V (SI unit: V) where ε= W Q where W = work done by source to drive a unit charge around the circuit where V= W Q where W = work done to drive a unit charge through a component Chapter 17 Current Electricity Electric current I (SI unit: A) related to (continued from previous slide) Resistance R (SI unit: Ω) where ρ= R= V I where V = potential difference I = current if constant URL related to resistivity ρ RA l where l = length A = cross-sectional area if not constant Obeys Ohm’s Law IαV Does not obey Ohm’s Law Ohmic conductors Non-ohmic conductors Chapter 17 Current Electricity The URLs are valid as at 15 October 2012. Acknowledgements (slides 1−47) plasma globe © Stuartkey | Dreamstime.com (slides 6, 15) battery © Vladwitty | Dreamstime.com (slides 6, 15) bulb © Monsieurpix | Dreamstime.com (slide 7) ammeter © Arsty | Dreamstime.com (slide 18) voltmeter © Arsty | Dreamstime.com (slide 22) circuit © Marshall Cavendish International (Singapore) Private Limited (slide 33) fixed resistors © Sergpet | Dreamstime.com (slide 33) rheostat © Arsty | Dreamstime.com