NYJC H2 Current of Electricity Lecture Notes

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 1 Chapter 13 CURRENT OF ELECTRICITY Content  Electric current  Potential difference (p.d.)  Resistance and resistivity  Sources of electromotive force (e.m.f.) Learning Outcomes Candidates should be able to: (a) show an understanding that electric current is the rate of flow of charge. □ □ □ (b) derive and use the equation I = nAvq for a current-carrying conductor, where n is the number density of charge carriers and v is the drift velocity. □ □ □ (c) recall and solve problems using the equation Qt I □ □ □ (d) recall and solve problems using WV Q □ □ □ (e) recall and solve problems using PV I , 2PR I and 2VP R □ □ □ (f) recall and solve problems using VR I □ □ □ (g) sketch and explain the I−V characteristics of various electrical components such as an ohmic resistor, a semiconductor diode, a filament lamp and a negative temperature coefficient (NTC) thermistor. □ □ □ (h) sketch the resistance-temperature characteristics of an NTC thermistor □ □ □ (i) recall and solve problems using R A  □ □ □ (j) distinguish between electromotive force (e.m.f.) and potential difference (p.d.) using energy considerations. □ □ □ (k) show an understanding of the effects of the internal resistance of a source of e.m.f. on the terminal potential difference and output power. □ □ □

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 2 The term “e lectricity” describes the set of physical phenomena associated with the presence and flow of electric charge . These phenomena include but are not limited to lightning, static electricity, electric current , and electromagnetic induction. Electricity is involved in powering household appliances, transportation devices, and industrial machineries; it is also used to transfer energy over large distances; and to send information via telecommunications. This chapter introduces concepts required for the following chapters: D.C. Circuits, Electric Fields, Electromagnetism, Electromagnetic Induction and Alternating Currents. 1 ELECTRIC CURRENT AND CHARGE Charge carriers (or charged particles) such as electrons, protons and ions carry either a positive or negative charge. An electric current is said to be present when there is a net flow of charge. 1.1 ELECTRIC CURRENT Symbol: I SI unit: Ampere (A) Definition of Electric Current Electric current is the rate of flow of charged particles. Calculating Current dQ dtI Where I is the current in amperes, Q is the charge in coulombs and t is the time elapsed in seconds. If the current is constant, Q tI Conventionally, the direction of current is the direction in which there is a net flow of positive charge carriers; it is opposite to the direction of net flow of negative charge carriers. The diagram below shows net movement of charge and the corresponding direction of current. Net +ve charge movement Net –ve charge movement Net +ve charge movement Net –ve charge movement No net movement of charge No net movement of charge no current

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 3 Drift velocity When no potential difference is applied across a conductor, its mobile charge carriers undergo random motion similar to gas molecules in the air as shown in Fig. 3a. The presence of a potential difference across the conductor alters this random motion such that while moving randomly, the mobile charge carriers also drift axially along the conductor as shown in Fig. 3b. This rate of change of axial displacement with respect to time is known as its drift velocity, vd. To relate current I to the flow of individual charges q, consider a small flow of charge ΔQ through a small segment of conductor with volume ΔV in a time interval Δt. The current in this segment is given by Q t  I . ΔQ = (ΔN)q The charge ΔQ is given by the product of the number of charge carriers Δ N and the charge q carried by each carrier, thus () Nq t  I ΔN = nΔV Let n be the number density of charge carriers (i.e. number of charge carriers per unit volume) . The number of charge carriers Δ N is the product of the number density of charge carriers n and the volume of the segment ΔV, thus ()n V q t  I ΔV = AΔx The volume of this segment of conductor Δ V is the product of its length Δ x and cross-sectional area A, thus ()nA x q t  I Since x t   is the average distance travelled by the charge carriers per unit time, we denote it as vd, the drift velocity of the charge carriers. Fig. 3a: Random motion (no potential difference) Fig. 3b: Random motion with axial drift (potential difference applied)

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 4 Hence, we can relate I and q as follows: Relationship Between Current And Drift Velocity The current carried by a conductor, I, is given by dnAv qI where n is the number density of charge carriers (number of charge carriers per unit volume), A is the cross-sectional area of the conductor, vd is the drift velocity, and q is the charge carried by each charge carrier. 1.2 ELECTRIC CHARGE Electric charge is the physical quantity of matter that causes it to experience an electric force when it is in the vicinity of other electrically charged matter. The nature of this electric force will be further elaborated in the topic on Chapter 14 Electric Field. Symbol: Q SI unit: Coulomb (C) Definition of electric charge The charge which flows pas t a point in time t is the product of current and time, if the current is steady. Definition of unit coulomb (not in syllabus) One coulomb is the amount of charge which flows past a point when a steady current of one ampere flows for one second. Calculating Total Charge from Current In general, Q dt I If the current is constant, Q = It Graphical Representation Consider a current, I, at a point in space over time, t. The charge Q which flows past this point in the time interval Δt is determined by the area bound by the t-axis and the I–t curve. Varying current Constant current

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 5 Charge is quantised, which means it cannot take on arbitrary values. The smallest quantity of charge that can be carried is 1.60 × 10−19 C, a value known as e, the elementary positive charge. A proton carries a charge of e, an electron carries a charge of −e; a helium nucleus carries a charge of 2 e, and so on. Example 1 A charging iPhone 7 draws a steady current of 1.00 A from the iPhone charger. (a) Given that the capacity of the iPhone 7’s battery is 7.06 × 103 C, determine how long it would take for the battery to charge fully. (b) The copper charging wire has a diameter of 0.511 mm, and the number density of charge carriers in the wire is 8.5 × 1028 m−3. Assuming that each charge carrier carries a charge of e = 1.60 × 10−19 C, determine the drift velocity of the charge carriers. The amount of charge entering and leaving each junction is the same (or conserved) i.e. charges do not accumulate or disappear. This implies that the current remains constant along one single conductor. Similar to energy, charges obey the law of conservation: charges cannot be destroyed or created.

9749 H2 PHYSICS; 8867 H1 PHYSICS Lecture Notes Nanyang Junior College 6 2 ELECTRIC POTENTIAL ENERGY AND POWER When connected in a circuit, charge carriers possess electric potential energy (or electrical energy). The electric potential energy of a charge carrier may change as other forms of energy (such as heat or chemical energy) are converted from it or to it. This section deals with the energy considerations in various parts of a closed circuit. 2.1 ELECTRIC POTENTIAL When such a circuit is connected to an electrical device (such as a bulb or television), c