Electricity

• Resistance is \(V\) divided by \(I\) at the point you are asked about — read both values off the graph and divide. The gradient of an I–V graph is not the resistance.
• Energy transferred per unit charge. Resistance is V over I at the point. More carriers, less resistance; more collisions, more resistance.

• 9.1.1 I can understand — understand that an electric current is a flow of charge carriers
• 9.1.2 I can understand — understand that the charge on charge carriers is quantised
• 9.1.3 I can recall — recall and use Q = It
• 9.1.4 I can use — use, for a current-carrying conductor, the expression I = Anvq, where n is the number density of charge carriers
• 9.2.1 I can define — define the potential difference across a component as the energy transferred per unit charge
• 9.2.2 I can recall — recall and use V = W / Q
• 9.2.3 I can recall — recall and use P = VI, P = I²R and P = V²/R
• 9.3.1 I can define — define resistance
• 9.3.2 I can recall — recall and use V = IR
• 9.3.3 I can sketch — sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp
• 9.3.4 I can explain — explain that the resistance of a filament lamp increases as current increases because its temperature increases
• 9.3.5 I can state — state Ohm's law
• 9.3.6 I can recall — recall and use R = ρL / A
• 9.3.7 I can understand — understand that the resistance of a light-dependent resistor (LDR) decreases as the light intensity increases
• 9.3.8 I can understand — understand that the resistance of a thermistor decreases as the temperature increases (it will be assumed that thermistors have a negative temperature coefficient)

Units, significant figures and working are part of the physics. Give a calculated answer to the same number of significant figures as the least precise data, or one more; keep full precision in the working and round only at the end; write the unit with every final answer. A fifth of the qualification is experimental: Papers 3 and 5 test AO3 only, and their questions may be set in contexts outside the syllabus content, so the practical work in this chapter is set out as method, recording, graphs and uncertainties rather than as theory.

• “The resistance of a lamp at 6.0 V is the reciprocal of the gradient of its I–V graph there.” Correct Resistance is \(R = V/I\) at the point: read \(V\) and \(I\) off the graph and divide. With \(I\) on the y-axis the gradient is \(I/V\), not \(V/I\), and even its reciprocal equals \(V/I\) only for a straight line through the origin. For the lamp in this chapter, \(6.0/0.36 = 17\,\Omega\), while \(1/\text{gradient} = 33\,\Omega\).
• “\(V = IR\) is Ohm's law.” Correct \(V = IR\) is the definition of resistance and holds for every component at every point. Ohm's law is the separate statement that, for a metallic conductor at constant temperature, \(I\) is directly proportional to \(V\) — that is, \(R\) stays constant.
• “\(A = \pi d^2\), and 0.315 mm squared is 0.0992 mm², so put 0.0992 into \(R = \rho L/A\).” Correct \(A = \pi d^2/4\), and convert to metres before squaring: \(d = 3.15 \times 10^{-4}\,\mathrm{m}\), \(A = 7.79 \times 10^{-8}\,\mathrm{m^2}\). 1 mm² is \(10^{-6}\,\mathrm{m^2}\), not \(10^{-3}\).
• “P.d. is the energy the charge has.” Correct The potential difference across a component is the energy transferred per unit charge — energy transferred from electrical to other forms as each coulomb passes through it.
• “The lamp lights the instant the switch closes, so the electrons must move very fast.” Correct Drift speeds in a metal are about \(10^{-4}\,\mathrm{m\,s^{-1}}\). The lamp lights at once because the free electrons all round the circuit, including those already in the filament, start drifting together.
• “A thermistor's resistance rises with temperature, like a metal's.” Correct For the thermistor in this syllabus (negative temperature coefficient) it falls, because heating releases more charge carriers. A metal's resistance rises because its number of carriers stays fixed while collisions increase.
• “In a metal, current is positive charge flowing from + to −.” Repair The carriers in a metal are free electrons, drifting from − to +. Conventional current is defined in the opposite direction, the way positive charge would flow.
• “A body can carry a charge of \(1.2 \times 10^{-19}\,\mathrm{C}\).” Repair That is \(0.75e\). Charge is quantised in whole-number multiples of \(e = 1.60 \times 10^{-19}\,\mathrm{C}\), so it cannot exist on an isolated body.
• “The lamp lights instantly, so the electrons move at nearly the speed of light.” Repair Drift speeds in a metal are about \(10^{-4}\,\mathrm{m\,s^{-1}}\). Every free electron in the circuit starts drifting at once, including those already in the filament.
• “The drift speed is the same all round a series circuit, because the current is.” Repair The current is the same; the drift speed is \(v = I/(Anq)\), so it is larger wherever \(A\) (or \(n\)) is smaller.
• “P.d. is the energy of the charge.” Repair The potential difference across a component is the energy transferred per unit charge — energy transferred in the component for each coulomb passing through it.
• “Resistance is the gradient of the I–V graph” (or its reciprocal). Repair Resistance is \(V/I\) at the point. The gradient of an I–V graph is \(I/V\), and its reciprocal equals \(V/I\) only for a straight line through the origin; on a lamp's curve at 6.0 V the reciprocal of the tangent's gradient is 33 Ω while the resistance is 17 Ω.
• “\(V = IR\) is Ohm's law.” Repair \(V = IR\) defines resistance for any component. Ohm's law says \(I \propto V\) for a metallic conductor at constant temperature.
• “A filament lamp's resistance increases because the current pushes harder.” Repair The temperature rises; the lattice ions vibrate with larger amplitude; the electrons collide with them more often; so \(V/I\) rises.
• “A diode conducts as soon as the forward p.d. is above zero.” Repair The current is negligible until the forward p.d. reaches about 0.6 V, then rises steeply. In reverse it is almost zero.
• “\(A = \pi d^2\).” Repair \(A = \pi r^2 = \pi d^2/4\), and convert millimetres to metres before squaring.
• “Resistivity is the resistance of the wire.” Repair Resistivity (Ω m) is a property of the material. Resistance (Ω) also depends on the length and the cross-sectional area.
• “A thermistor's resistance rises with temperature, like a metal's.” Repair For the negative temperature coefficient thermistor in this syllabus it falls, because heating releases more charge carriers.
• “The percentage uncertainty in the area is the same as in the diameter.” Repair \(A \propto d^2\), so the percentage uncertainty is doubled: 1.8% in \(d\) becomes 3.6% in \(A\).
• “The main source of error was human error.” Repair Name the quantity and the reason: the diameter, whose 1.8% uncertainty (half the range of the micrometer readings) is doubled to 3.6% in the area.

• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.
• Interleave with the chapters that use this one. Topic 10 (D.C. circuits) builds circuits from these components: when you reach its potential dividers, re-answer "why does an LDR’s resistance fall in light?". Topic 18 turns "energy per unit charge" into electric potential at a point: re-state the definition of p.d. first. Topic 20 puts I = Anvq back in a magnetic field: re-derive it before you start. Recalling a topic inside a new context is worth more than another pass over this chapter on its own; at A Level, Paper 4 assumes the whole of the AS content, so nothing here is ever finished with.

• Cambridge International AS & A Level Physics 9702 has five components. Topic 9 is AS Level content, so it is examined in Papers 1, 2 and 3. AS Level content: examined in Paper 1 (multiple choice), Paper 2 (AS structured) and, as practical context, Paper 3. Assumed knowledge for Papers 4 and 5. AS Level candidates take Papers 1, 2 and 3; A Level candidates take all five, either staged over two years (Papers 1–3 in year one, Papers 4 and 5 in year two) or together in one series. Examinations are available in the June and November series, and in March in India.
• Across both the AS Level and the A Level the assessment objectives are weighted AO1 40% (knowledge and understanding), AO2 40% (handling, applying and evaluating information) and AO3 20% (experimental skills and investigations). AS candidates are graded a–e; A Level candidates A*–E. The Data and formulas sheet is printed as page 2 of Papers 1 and 2 and as pages 2 and 3 of Paper 4: it gives the constants and a short list of formulas. Every other equation in this chapter is one the syllabus says you must recall, and this chapter says which is which.
• A multiple-choice item on this topic (Paper 1) can turn on a single step: a diameter not squared or not converted from millimetres, a gradient read as a resistance, the wrong current put into \(I^2R\), a drift speed in a thinner wire. A structured question (Paper 2) can ask you to define potential difference or resistance, state Ohm's law, sketch a characteristic with its key features, and explain the filament lamp or a sensor in terms of charge carriers.
• Only \(I = Anvq\) is printed on the Data and formulas sheet, together with \(e = 1.60 \times 10^{-19}\,\mathrm{C}\). \(Q = It\), \(V = W/Q\), \(P = VI\), \(P = I^2R\), \(P = V^2/R\), \(V = IR\) and \(R = \rho L/A\) are all recall. The calculations chain them: charge, then number of electrons, then energy; power, then current, then resistance; diameter, then area, then resistance.
• The resistivity of a wire is this topic's Paper 3 context: vary the length between two clips, find \(R = V/I\) with an ammeter and a voltmeter, plot \(R\) against \(L\) and take \(\rho\) from the gradient times the area. The diameter, measured with a micrometer, carries the largest uncertainty, doubled in the area. An I–V characteristic or a thermistor against temperature is a Paper 5 planning context.
• Read the command word before you decide how much to write. This syllabus has fifteen of them: calculate, comment, compare, define, describe, determine, explain, give, identify, justify, predict, show (that), sketch, state and suggest. Define wants a precise meaning — for a physical quantity, usually an equation in words with every quantity named. State and give want a fact and nothing more. Describe wants the points or the features. Explain wants the reasons and the relationships — a describe-level answer to an explain question is incomplete however well written it is. Show (that) gives you the result and asks for the structured evidence that leads to it, so every step must appear — and a final value worked to one more significant figure than the one printed makes it plain that you calculated it rather than copied it. Sketch wants a freehand graph with its key features — intercepts, asymptotes, the shape — correct, but no plotted scale.