EJC Physics H214 Current of Electricity - 1. Notes-2023 (Full)

One of William Gilbert’s (1544 - 1603) contribution to the field of science was his study on static electricity. He established the “amber effect” (now called the triboelectric effect) – that certain materials such as amber can become electrically charged by friction with other materials. As Amber is called elektron in Greek, and electrum in Latin, Gilbert decided to refer to the phenomenon by the adjective “electricus”, giving birth to the word “electricity”. Content • Electric current • Potential difference • Resistance and resistivity • Electromotive force Learning Objectives: 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.

Previously from oscillations through waves, w e used a simplified microscopic model of individual particles oscillating and linked them to the macroscopic behaviour of wave properties. The study of the large-scale behaviour saves us the effort of having to model all of the individual behaviour of particles, and allows u s to investigate interactions and changes, such as multiple waves meeting and overlapping with each other. Here we study the macroscopic behaviour of electrons flowing through components and wires. When an electrical conductor is conducting electricity, an electric current is said to flow through it. This current is made up of a net flow of charged carriers (or charged particles) such as electrons ( negatively charged ), protons (positively charged) or ions (either polarities). Unless specified, conventional flow is assumed when working with current flow. Current is a scalar quantity; it does not obey vector addition laws. Electric current I is one of the 7 base S.I. quantities and has the S.I. unit of Ampere (A). It is chosen as a base quantity because it is easier to define the unit of electric current (from the macroscopic model)), than to derive the coulomb from the flow of charged particles (microscopic mode). Since current is the rate of flow of charge d d Q t=I . For constant current: and Q Qtt= =I I . Electrical resistance is one example of a macroscopic behaviour manifesting from the microscope model of individual electrons colliding with the vibrating lattice of metallic ions. conventional current flow electron flow Electric current is the rate of flow of charge

Drift velocity v is the net velocity of charge carriers in a certain direction under an externally -applied electric field. We distinguish this from thermal velocity, which is the random, haphazard motion in which there is no net direction (similar to Brownian motion). Thermal velocity does not contribute to current because the statistical average is zero in terms of net flow. Electrons in metals exhibit such random, haphazard motion because they are delocalised from the metal atoms (which form a giant lattice of metal cations), and make up a sea of free, delocalised electrons. The electrons collide with the lattice or amongst themselves, giving rise to resistance. Derivation For a current I in a wire that causes the charge carriers to have a drift velocity v, derive an equation relating current to the number density of charge carriers in the wire n, the cross sectional area of the wire A and the charge on each charge carrier q. Solution For a wire segment of length L, total charge in this volume is ( ) ( ) number of charge carriers in volume volume Qq n q nALq = = = Time taken t for charge carriers to have net displacement of L L vt= Current is the rate of flow of charge nALq L / v Q nAvqt ===I For a current-carrying conductor, nAvq=I I : current (A) n : number density of charge carriers (m-3) A : cross sectional area (m-2) V : drift velocity (m s-1) q: charge (C)

drift velocity thermal agitation zero when there is no potential difference across conductor zero in terms of statistical average individually zero only at temperature of 0 K associated with net flow of charge carriers results in zero net flow of charge carriers does not contribute to current speed ~ 10-4 m s-1 speed ~ 105 m s-1 Example 1 A copper wire of diameter of 0.500 mm carr ies a current of 1.0 A. Estimate the number density of free, delocalised electrons in the wire. Solution Assuming all charge carriers are free delocalised electrons: ( ) ( )( ) 22 23 4 19 29 3 10 1 6 10 3 2 10 2 1 m 05 102 r . . nAvq n Avq vq d vq .    − −− − ==     = =      =  I I I I Example 1 illustrates 2 important concepts: • An electron that contributes to current moves at about 10 -4 m s-1; it may take forever for an electron to travel from a battery to a light bulb, but it doesn’t need to. • An electron carries a small finite amount of charge 191 6 10 Cq . −= but there are many moving (albeit slowly) at the same time. E Why does the lightbulb light up almost immediately when the switch is closed? When a circuit is closed, the electric field inside the circuit is set up almost instantaneously so that all electrons in wire and bulb filament start to move at the same time.

When the terminals of a battery are connected across an electrical component (such as a light bulb or resistor), current flows through th e component from the point of higher electric potential to the point of lower electric potential. Recall that gravitational potential refers to the work done per unit mass in bringing a small test mass from infinity to that point. Instead of a unit mass (as per a gravitational field), for circuits we reference a unit charge. Example 2 An electric runs off a 230 V supply for 15 minutes, during which it produced 720 kJ of heat. (a) Find the amount of charge that flow through the heating element. (b) State an assumption that you have made in your calculations for part (a). Solution Assuming that all electrical energy is converted to heat at 100% efficiency, 310720 2 3130 C30 W Q W V Q V == = = Electromotive force (e.m.f.) is the energy transformed from chemical to electrical per unit charge when charge is driven round a complete circuit. *e.m.f. is not a force. It is scalar as it does not obey vector addition, and exists with or without current flow chemical (stored) energy electrical energy sound light heat Potential difference (p.d.) is the energy transformed from electrical to other forms per unit charge when charge passes through an electrical component. V: potential difference (V) W : work done (J) Q : charge (C) We can regard “electrical energy” as the medium of transfer from stored energy in a source of e.m.f. to energy that is dissipated in devices. E I electrical component