DHS 09 Current of Electricity (Lecture Notes & Tutorial)

Dunman High School (Senior High Physics) 1 Topic 9 Current of Electricity Guiding Questions: • How does the macroscopic phenomenon of current flow relate to the movement of microscopic charges? • How are current, voltage, and resistance related in an electrical circuit? • What happens to energy in an electrical circuit? Content • Electric current • Potential difference • Resistance and resistivity • Electromotive force 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 Q = It (d) recall and solve problems using the equation V = W / Q (e) recall and solve problems using the equations P = VI, P = I2R and P = V2 / R (f) define the resistance of a circuit component as the ratio of the potential difference across the component to the current passing through it and solve problems using the equation V = IR (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 characteristic of an NTC thermistor (i) recall and solve problems using the equation R = ρl / 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.

Dunman High School (Senior High Physics) 2 Introduction Charge is a property possessed by some (but not all) elementary particles (e.g. electrons, protons). Charge is found as two types, positive and negati ve, which ‘neutralise’ one another if brought together in equal quantities. Objects that have an electrical charge exert electrostatic forces on each other. The SI unit used to measure electrical charge is the coulomb (C). Physicists used to think that electrical charge could only be found in whole number multiples of a fundamental amount of charge, e = 1.602192 × 10−19 C. Charge on the proton = +e Charge on the electron = −e However, in the late 1960s, small particles called quarks were discovered with electric charge of either 2 3 e+ or 1 3 e− . These, together with –e, seem to be the basic quantities of electric charge. (a) show an understanding that electric current is the rate of flow of charge (c) recall and solve problems using the equation Q = It Electric current (SI base unit: ampere ), consists of charges in motion from one region to another. When this motion takes place within a conducting path that forms a closed loop, the path is called an electric circuit. In metals, current is due to the flow of electrons which carry negative charges . It should be noted, however, that the direction of the current is, by convention, the direction that positive charges move. At room temperature, metals such as copper or iron have electrons that are free to move within the physical constraints of the material. These free electrons move randomly in all directions, somewhat like the molecules of a gas but with much greater speeds (of the order of 106 m s−1). Electric current flowing through a cross-section of a conductor is the rate of flow of charges through it. Hence, the instantaneous current passing through a cross section of the conductor at a given time is given by dQ dt=I + + + + + _ _ _ _ _ Direction of electric current

Dunman High School (Senior High Physics) 3 If the electric current I is steady, then the total amount of charge Q which flows past a point in a time duration t would be given by Qt= I Example 1 The diagram on the right shows a model of an atom in which two electrons move round a nucleus in a circular orbit. The electrons complete one full orbit in 1.0 × 10−10 s. What is the current caused by the motion of the electrons in the orbit? Example 2 A high potential is applied between the electrodes of a discharge tube so that the gas is ionized. Electrons and positive ions move towards the positive and negative electrodes respectively. In each second, 5 × 1018 electrons and 2 × 1018 singly charged positive ions pass a cross-section of the tube. Determine the current flowing in the discharge tube. (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 The diagram shows a current passing through a cross section of a wire. Each positive charge carrier has charge q and there are n charge carriers per unit volume. Their average drift velocity is v. One section of the wire has been magnified. Its cross-sectional area is A. nucleus electron electron I I q v P

Dunman High School (Senior High Physics) 4 Current = rate of flow of charge = (number of charge carriers per unit time) × (charge on each carrier) The number of charge carriers per unit time passing a point (P) in the wire is equal to the number contained in a volume of wire with length v. nAv nAvq number of charge carriers per unit time Thus the current in wire is ∴= =I Note • The thinner the wire (for the same current) the faster the charge carriers must move. • If current is increased, the only term that can increase is v. • For the same length of wire, greater cross-sectional area allows more room for charge carriers, leading to more current. Drift velocity v Thermal energy makes free charge carriers move about at high speeds (of the order of 10 6 m s–1). The collisions between electrons and metal ions are frequent and random. Thermal motion does not carry the electron any distance along the wire. Under the influence of a potential difference applied across the conductor, the charge carriers gain an additional drift motion that carries them along the conductor (at the order of 10–4 m s–1) and as a result, charge is transferred. The direction of this drift is not random, as they are being directed by the field lines from the cell. This is the drift velocity.

Dunman High School (Senior High Physics) 5 Example 3 The number of free electrons per cubic metre in a copper wire is approximately 8.0 × 1028, that is, about 1 or 2 free electron per atom. A typical diameter of wire is 1.0 mm. If the current is 1.0 A, what is the average speed of the electrons along the wire? Example 3 shows how slowly electrons drift (often in the order of 10−4 m s−1) along a wire, but there is no time delay between turning on a light switch and the light coming on. This is because the electric field is set up in the wire with a speed approaching the speed of light, and all the electrons start to move all along the wire at very nearly the same time. The time that it takes any individual electrons to get from the switch to the light bulb is not relevant. A common misconception is that when a lamp, for example, is switched on, electrons somehow rush round to the lamp at a very high speed, hence it illuminates instantaneousl y. The magnitude of the drift velocity shows that this is quite clearly not the case. We should regard the connecting wires as being already ‘full’ of electrons all the way round the circuit and switching on merely starts the slow flow for all, rather like turning on a tap to start water flowing in ‘full’ water pipes. Analogy between waterfall and lighting circuit Consider the analogy of the human powered waterfall to a simple lighting cir