RI Chap 15 Currents Notes

15 CURRENTS H2 Physics 9478 Content Page 15.1 Current and drift velocity 2 15.2 Potential difference, electromotive force and power 5 15.3 Power supplies: d.c. and a.c. 7 15.4 Appendix 17 Learning Outcomes Candidates should be able to: (a) show an understanding that electric current is the rate of flow of charge and solve problems using Q t=I . (b) derive and use the equation nAvq=I 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 for potential difference in terms of electrical work done per unit charge, WV Q= . (d) recall and solve problems using the equations for electrical power PV= I , 2PR= I and 2VP R= . (e) distinguish between electromotive force (e.m.f.) and potential difference (p.d.) using energy considerations. (f) show an understanding of and use the terms period, frequency, peak value and root-mean-square (r.m.s.) value as applied to an alternating current or voltage. [not in H1 syllabus] (g) represent a sinusoidal alternating current or voltage by an equation of the form 0 sinxx t ω= . [not in H1 syllabus] (h) deduce that the mean power in a resistive load is half the maximum (peak) power for a sinusoidal alternating current. [not in H1 syllabus] (i) distinguish between r.m.s. and peak values, and recall and use 0 r.m.s. 2 = II and 0 r.m.s. 2 VV = for the sinusoidal case. [not in H1 syllabus] (j) explain the use of a single diode for the half-wave rectification of an alternating current. [not in H1 syllabus]

Page | 2 Introduction Direct current (d.c.) is the unidirectional flow of electric charge. This flow of electric charge in a constant direction distinguishes it from the alternating current (a.c.). Such direct currents are produced by sources such as batteries and solar cells. Direct current may also be obtained from an alternating current supply by the use of a rectifier, which allows current in one direction only. Similarly, direct currents can also be converted into alternating currents with the use of an inverter. The first commercial electric power transmission that was developed by Thomas Edison in the late 19th century used direct current. Today, direct current is used in rail transport, electric vehicles, general electrical appliances, as well as to charge batteries. 15.1 Current and drift velocity  Charge and electric current The SI unit of charge is the coulomb (C), named after the French physicist Charles-Augustine de Coulomb (1736−1806). Charge is related to the electric current I by the equation: Q t=I where Q is the amount of charge that passes through the cross section at any point of a conductor in time t. Direction of current is the direction of flow of positive charges. Hence, electrons moving to the left gives rise to current to the right. Shock and Awe: The Story of Electricity Electric current is measured in ampere (A), named after the French physicist André Ampère (1775−1836). If the rate at which charge flows varies with time, the instantaneous current I is defined as dQ dt=I . When a constant current I flows through a cross-section of a conductor for a duration t, the amount of electrical charge Q passing through it is Qt= I . If the current flow is not constant, Q dt=∫I . By convention, the direction of current is defined as the direction of flow of positive charge, regardless of the actual sign of the charged carriers. Positive charges flow from the positive terminal to the negative terminal outside of a cell (i.e. from negative to positive terminal within a cell). 1 C = 1 A s, i.e., coulomb is an ampere second. A continuous conducting path, i.e., a complete circuit, is required for there to be an electric current in a circuit. Electric current Electric current is the rate of flow of charge.

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 3 Example 1 Which diagram shows the direction of the current I and the direction of electron flow e in a circuit? [Solution] Direction of current is the direction in which positive charges move, i.e., in the ______________ direction. Electrons move in the _____________ direction, i.e., in the ________________ direction, as they move from the __________terminal to the _________ terminal outside of the cells. Answer:

Page | 4  Drift velocity In the absence of an electric field, the conduction or free electrons in a metal conductor move randomly and undergo frequent collisions with the positive ions that form the crystal lattice. The electrons do not, on average, move in any particular direction and there is no current. The magnitude of the velocity of the random m otion is of the order of 106 m s−1. When an electric field is applied to the conductor, the electrons continue to move randomly but with a net motion or drift in the direction opposite to that of the electric field. This motion is described in terms of the drift velocity of the electrons. The magnitude of the drift velocity is of the order of 10−4 m s−1 or less. Consider a current -carrying conductor with charge carriers each of charge q, number density of charge carriers n and cross-sectional area A. Assume that all charge carriers move with the same drift velocity v. In time t, each charge carrier in the conductor travels a distance  , where vt= . Hence, charge carriers within a cylinder of length  and volume V will pass through a cross-section A of the conductor in time t. Fig. 15.1 From the definition of electric current, ( ) ( ) ( ) ( ) Q t Nq Q Nqt nV q NntV nA q VAt nAvq v t = = = = = = = = =  I      where N is the total number of charge carriers that pass through the cross section of the conductor in time t. Number density is the number of charge carriers per unit volume. Drift Velocity Derivation - A Level Physics A light bulb turns on almost immediately after a switch is closed (despite such a slow drift velocity) because closing the switch establishes an electric field almost immediately throughout the circuit, causing the free electrons in the entire circuit to move almost instantly. On the other hand, it may take hours for a charge to move all the way round a circuit. A +q +q +q +q I cross-section of a conductor v

RAFFLES INSTITUTION YEAR 56 PHYSICS DEPARTMENT Page | 5 15.2 Potential difference, electromotive force and power  Potential difference (p.d.) The SI unit for electric potential and electric potential difference is the volt (V), named after Italian physicist Alessandro Volt (1745−1827). Electrical work W is done when charges Q are moved across two points with potential difference V , transferring energy from electrical from to other forms. Mathematically, WV Q=  Electromotive force (e.m.f.) The sources of energy that cause charges to move in electric circuits are called sources of electromotive force. A source of e.m.f. is a device that maintains a potential difference across a conductor. Examples of sources of e.m.f. are batteries, electric generators and solar cells. E.m.f. shares the same SI unit as p.d., i.e., the volt (V). Electric potential difference is colloquially known as voltage as it is measured in volts. 1 V = 1 J C−1, i.e., volt is joule per coulomb. Electromotive force is not a force. A cell is a source of constant e.m.f. and not a constant source of current or terminal voltage. A cell does not create or destroy any charge, i.e., a cell does not supply or absorb electrons, nor does a resistor absorb or destroy charge.  Comparing p.d. and e.m.f p.d. V across an external load e.m.f. E of a source WV Q= WE Q= W is the energy converted from electrical