Currents Of Electricity JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS CURRENT OF ELECTRICITY Content 1 Electric current 2 Potential difference 3 Resistance and resistivity 4 Electromotive force Learning Outcomes Students 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 = 2V 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 electric al 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 = A l . (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 resistanc e of a source of e.m.f . on the terminal potential difference and output power.

2 Introduction • In everyday life, we are familiar with electric currents flowing in wires and other conductors. Electric current is said to be set up along a conductor when there is a flow of charges in a particular direction. • We first examine electric current from a macroscopic point of view: i.e. current measured using laboratory apparatus. Then, we examine it from a microscopic point as flows of electrons and their drift velocity. • Fig. 1.1 shows a circuit diagram where a direct current is flowing, driven by a cell. It also shows electrons in the wire moving away from the negative terminal (since electrons are negatively-charged and we know that like charges repel) and move towards the positive terminal (since unlike charges attract) of the cell. Fig. 1.1 Electron movement in an electric circuit Note: ❖ Scientists first thought that positive charges flow from the positive terminal of a cell to the negative terminal. This is the conventional current direction. The d irection of conventional current is thus the direction of the flow of positive charges in a circuit. ❖ However, it was later found that a current in a metal wire is in fact a flow of negatively - charged electrons in the opposite direction. That is, electrons flow from the negative (−) to the positive (+) terminal outside the battery. ❖ Nevertheless, the conventional current is still being used. ❖ When solving problems involving circuit diagrams , it is the conventional current (and not the electron flow) that is indicated on the circuit diagrams . Its direction is from the positive (+) to the n(−) terminal outside the battery as shown in Fig. 1.2. Fig. 1.2 Conventional current in an electric circuit conventional current electron flow + – - + R electrons moving through copper wire

3 1 Electric Current (a) To show an understanding that electric current is the rate of flow of charge. (c) To recall and solve problems using the equation Q = It. 1.1 Charge and the coulomb • Charge Q refers to a quantity of electricity. • Charge flowing past a given cross-section of a conductor is the product of the steady current and time during which the current flows. • The SI unit of charge is the coulomb (C). • The coulomb is the quantity of charge which passes a given cross-section in one second when a current of one ampere is flowing, i.e. 1 C = 1 A s. • e is the elementary charge, and it has a magnitude of 1.60  10−19 C. • Protons and positive ions are positively -charged particles. Charge of a proton is +1.60  10−19 C or +e. • Electrons and negative ions are negatively -charged particles. Charge of an electron is −1.60  10−19 C or –e. 1.2 Flow of charged particles • Positive particles move from a position of high potential (+) to a position of low potential (−). Negative particles move from a position of low potential (−) to a position of high potential (+). The flow of charged particles constitutes an electric current , denoted by the symbol I. • The SI unit of electric current is the ampere (A). • The electric current I is the rate of flow of charge. dQ dt=I Amount of charge Q dt= I = area under I-t graph, shown in Fig. 2. Fig. 2 Variation of current I (non-constant) with time I / A t / s

4 • A constant current exists when there is a constant rate of flow of charge. • For constant current, I = Q t Amount of charge Q = It = area under I-t graph, as shown in Fig. 3. Fig. 3 Variation of current I (constant) with time Example 1 Calculate the (steady) current in a circuit when a charge of 40 C passes in 5.0 s. Solution: I = Q t = 40 C 5.0 s = 8.0 A Example 2 A car battery is used to supply a varying current. Calculate the total charge delivered from the battery if the variation in current supplied with time is given by the graph as shown on the right. Solution: Total charge, Q = area under I-t graph Q = 1 2 (3 + 5)  20 = 80 C • For a constant current, I = Q t . • If N is the number of charged particles passing a cross-section of a conductor in time t, and q is the charge of each charged particle, the total charge flow is Q = Nq. • Thus, I = Q Nq N qt t t ==  . • N t is the number of charged particles per unit time passing through a cross-section of the conductor. I / A t / s I t 1 2 3 4 5 6 7 0 10 20 30 I/A t/s

5 Example 3 Determine the number of electrons are passing through a wire per second if the current is 1.00 mA? Solution: I = Ne t → I=N te − − =  3 19 1.00 10 1.60 10 = 6.25  1015 s−1 • Fig. 4 shows o ppositely-charged pa rticles in a gas or liquid moving in opposite directions under the influence of an electric field. Fig. 4 Charged particle movement in a gas or liquid, under influence of electric field Example 4 A high potential is applied between the electrodes of a hydrogen discharge tube so that the gas is ionised. Electrons then move towards the positive electrode and protons towards the negative electrode. In each second, 5 .0  1018 electrons and 2 .0  1018 protons pass a cross-section of the tube. Determine the current flowing in the discharge tube. Solution: Total number of charged particles passing in 1 s, N t = (5.0 + 2.0)  1018 = 7.0  1018 s−1 Current passing the tube, I = Q t = Ne t = (7.0  1018)(1.60  10−19) = 1.12 A + + + + • + high potential + - - - - - - low potential − +

6 v 1.2.1 Flow of charges in a metallic conductor • Fig. 5 shows free (mobile) electrons within the lattice structure of a metallic conductor, e.g. a copper wire. • The electrons wander randomly and haphazardly among the metal atoms/ions of the lattice structure. Fig. 5 Free electrons within the lattice structure of a metallic conductor • The net flow of charge is zero and thus, there is no current. • Focusing on a single electron, its net displacement after multiple collisions with the metal atoms is also zero, as shown in Fig. 6. Fig. 6 Zero net displacement of an electron a