ASRJC Current of Electricity

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 14-1 Additional Notes Topic 14: Current of Electricity Content A Electric Current B Potential Difference C Resistance and Resistivity D Power and Heating Effect E Sources of 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 =V I, 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 = l / 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

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 14-2 Additional Notes A Electric Current A.1 Electric Charge, Q • The electric charge is a property of some elementary particles (such as electrons and protons) that gives rise to an interaction between them / causing them to attract and repel each other. • The charge of an atom arises as a result of an excess or deficit of electrons with respect to protons in the atom. If the atom gains or loses an electron, it becomes charged and is called an “ion”. • The smallest known electric charge is the elementary charge e. proton charge, e = 1.60 × 10–19 C electron charge, −e = −1.60 × 10–19 C • Subsequently, any charge Q can be quantized as a multiple of the elementary charge, Q = Ne where N = number of charge particles • The SI unit of charge is coulomb (C). One coulomb is that charge flowing per second past a point in a circuit in which the current is 1 ampere. The electric charge ΔQ passing one point in a circuit in an interval of time Δt is given by ΔQ = I Δt for a constant electric current I in the circuit. charge in coulombs = (current in amperes) × (time in seconds) ➔ ∆Q = I ∆t • If the current is not constant in a circuit then the charge which flows can be found by using the area beneath the current-time graph. In calculus terms this can be written as ➔ dQt=  I Example 1 Determine the number of electrons that will make up −1.0 C. In the definition of a coulomb, a unit, it is defined in terms of other units. Note that N must be a positive integer. The definition of electric charge, a physical quantity, is in terms of other physical quantities. The data for the elementary charge, e = 1.60×10−19 C, is given in the list of data in exam. Graphically, the charge, ∆Q, can be found from the area under I−t graph.

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 14-3 Additional Notes Example 2 The current through an electrical component is reduced uniformly from 100 mA to 20 mA over a period of 8.0 s. Determine the charge that flows through the electrical component during the 8.0 s. A.2 Electric Current, I Electric current (I) is the rate of flow of charge (which may be positively or negatively charged). • The current I can be mathematically expressed as I = dQ dt where dQ = amount of charge that passes through cross-section dt = amount of time in which dQ passes through • The S.I. unit for current is ampere (A), which is also a base unit. • By convention, current I refers to the flow of positive charges. • When negatively charged particles flow (i.e. in an electric circuit) in a given direction, it is equivalent to a conventional current I flowing in the opposite direction. Flow of Particles Conventional Current, I equivalent to equivalent to equivalent to For steady current, the amount of charge passing through a point in a given time is constant. Hence, the equation becomes I = Q / t. memorise

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 14-4 Additional Notes Example 3 The diagram above shows a hydrogen discharge tube. A high potential difference is applied between the electrodes of the discharge tube so that the hydrogen gas is ionized. 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. Calculate the current flowing in the discharge tube. Example 4 The diagram 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 1.0×10−15 s. Calculate the current caused by the motion of the electrons in the orbit. p e − + nucleus electron electron I

ANDERSON SERANGOON JUNIOR COLLEGE PHYSICS 9749 14-5 Additional Notes A.3 Microscopic Model of Current • In the absence of an external electric field, the mobile charge carriers ( which can be either positively or negatively charged particles) in a conductor move randomly in all directions, somewhat like the molecules of a gas. • Since the motion of the charge carriers is random, there is no net flow of charge in any direction and hence, no current. • When a constant, steady electric field is applied across the conductor, the mobile charge carriers are subjected to a steady electric force. IF they are moving in a vacuum, this steady force will cause them to have a steady acceleration in the direction of the force. • But a mobile charge carrier in a conductor undergoes frequent collisions with the massive atomic cores of the material. In each such collision, the carrier’s direction of motion undergoes a random change. • The net effect of the electric field is that there is a net motion or drift of the mobile charge carriers in the direction of the electric force, on top of the random motion. This motion is termed the drift velocity of the charge carriers. As a result, there is net current in the conductor. (Refer to animation in slideshow) A.4 Derivation of I = nAvq for a current-carrying conductor • Consider a current-carrying conductor of uniform cross-sectional area A, and having a number density of charge carriers n. • Each of the charge carrier has a charge q. • Due to the presence of an electric field, the charge carriers have a drift velocity v. Path of mobile charge carrier without electric field. They move randomly. Path of mobile charge carrier with electric field. The motion is still random, but there is a net drift to the right. mobile charge carrier In an electric field, the positive mobile charge carriers will have a drift velocity in the same direction as that of the field. For negative charge carriers, the direction of drift velocity is opposite to the direction of the electric field. An electric field is a region of space where charges experience an electric force, similar to how a mass experiences a gravitational force in a gravitational field. One method to obtain an electric field in a conductor is to connect its ends to plates of different po