D.C. circuits

• A voltmeter reads the e.m.f. only when no current flows. Charge at a junction, energy round a loop.
• Energy per unit charge, in or out. V = E − Ir. Charge at a junction, energy round a loop. Zero current, no lost volts, e.m.f.

• 10.1.1 I can recall — recall and use the circuit symbols shown in section 6 of this syllabus
• 10.1.2 I can draw — draw and interpret circuit diagrams containing the circuit symbols shown in section 6 of this syllabus
• 10.1.3 I can define — define and use the electromotive force (e.m.f.) of a source as energy transferred per unit charge in driving charge around a complete circuit
• 10.1.4 I can — distinguish between e.m.f. and potential difference (p.d.) in terms of energy considerations
• 10.1.5 I can understand — understand the effects of the internal resistance of a source of e.m.f. on the terminal potential difference
• 10.2.1 I can recall — recall Kirchhoff's first law and understand that it is a consequence of conservation of charge
• 10.2.2 I can recall — recall Kirchhoff's second law and understand that it is a consequence of conservation of energy
• 10.2.3 I can — derive, using Kirchhoff's laws, a formula for the combined resistance of two or more resistors in series
• 10.2.4 I can use — use the formula for the combined resistance of two or more resistors in series
• 10.2.5 I can — derive, using Kirchhoff's laws, a formula for the combined resistance of two or more resistors in parallel
• 10.2.6 I can use — use the formula for the combined resistance of two or more resistors in parallel
• 10.2.7 I can use — use Kirchhoff's laws to solve simple circuit problems
• 10.3.1 I can understand — understand the principle of a potential divider circuit
• 10.3.2 I can recall — recall and use the principle of the potentiometer as a means of comparing potential differences
• 10.3.3 I can understand — understand the use of a galvanometer in null methods
• 10.3.4 I can explain — explain the use of thermistors and light-dependent resistors in potential dividers to provide a potential difference that is dependent on temperature and light intensity

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.

• “A voltmeter across a battery reads its e.m.f.” Correct A voltmeter reads the e.m.f. only when no current flows. While the cell supplies a current I it reads the terminal p.d., V = E − Ir, which is smaller. See 10.1.5.
• “E.m.f. and p.d. are the same thing, because both are in volts.” Correct Both are energy per unit charge, but in opposite directions: e.m.f. is energy converted to electrical form in a source; p.d. is electrical energy converted to other forms between two points. See 10.1.4.
• “Kirchhoff's first law is conservation of energy.” Correct First law, junctions, charge; second law, loops, energy. See 10.2.1 and 10.2.2.
• “1/R = 1/4 + 1/12 = 1/3, so R = 0.33 Ω.” Correct That sum is 1/R. Invert it: R = 3 Ω. A parallel combination is always smaller than its smallest resistor, which is a free check. See 10.2.6.
• “A current came out negative, so I have made a mistake.” Correct A negative current means it flows opposite to the direction you assumed. Keep the value and state the true direction. See 10.2.7.
• “When the thermistor warms up, the output of the divider rises.” Correct It rises if the output is across the fixed resistor and falls if it is across the thermistor. Say which one the output is across before you say which way it moves. See 10.3.4.
• “At the balance point the galvanometer current is largest.” Correct It is zero. That is the whole point: with no current in the test cell there is no p.d. across its internal resistance, so the e.m.f. itself is balanced. See 10.3.3.
• “E.m.f. is the force that pushes the current round the circuit.” Repair E.m.f. is not a force. It is the energy transferred per unit charge in driving charge around a complete circuit, measured in volts.
• “E.m.f. and p.d. are the same, because both are measured in volts.” Repair Same unit, opposite energy transfers: e.m.f. is other forms converted into electrical energy per unit charge, in a source; p.d. is electrical energy converted into other forms per unit charge, between two points.
• “A voltmeter across a battery always reads its e.m.f.” Repair Only when no current flows. While the battery supplies a current I the voltmeter reads the terminal p.d., E − Ir.
• “Reducing the external resistance raises the terminal p.d., because more current flows.” Repair More current means more lost volts Ir, so V = E − Ir falls.
• “The gradient of the V–I graph is the internal resistance.” Repair The gradient is −r; r is minus the gradient. The intercept on the V-axis is E.
• “Kirchhoff's first law is conservation of energy and the second is conservation of charge.” Repair Swapped. First law (junctions): charge. Second law (loops): energy.
• “Going round the loop I passed the cell from + to −, so I counted its e.m.f. as positive.” Repair Passing through a source from + to − counts its e.m.f. as negative; from − to + counts it as positive.
• “Adding a resistor in parallel increases the total resistance.” Repair It adds a path. The total resistance falls, below the smallest branch, and the total current rises.
• “1/R = 1/4 + 1/12 = 1/3, so R = 1/3 Ω.” Repair Invert at the end: R = 3 Ω.
• “I2 came out as −0.67 A, so I must have made an error.” Repair The minus sign means the current flows opposite to the direction assumed. The size, 0.67 A, is correct; state the true direction.
• “In a potential divider the smaller resistor gets the larger p.d.” Repair Same current, V = IR: the larger resistor has the larger p.d.
• “Vout = VinR2/(R1 + R2) whatever is connected to the output.” Repair Only if no current is drawn, or the load is much larger than R2. A load in parallel with R2 lowers Vout.
• “At the balance point the galvanometer current is at its maximum.” Repair It is zero. With no current in the test cell there is no p.d. across its internal resistance, so its e.m.f., not a terminal p.d., is balanced.
• “The test cell can be connected either way round on the potentiometer.” Repair Its positive terminal must go to the same end of the wire as the driver cell's positive terminal, or there is no balance point.
• “It is warmer, so the thermistor divider's output rises.” Repair It rises across the fixed resistor and falls across the thermistor. Say which one the output is across.
• “The ammeter goes across the lamp to measure its current.” Repair Ammeters in series, voltmeters in parallel.

• 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.
• Writing the distinction. A complete answer names both directions: “e.m.f. is the energy converted from other forms into electrical energy per unit charge by a source; p.d. is the energy converted from electrical energy into other forms per unit charge between two points.” Saying only that one is “for a cell” and the other “for a resistor” does not mention energy at all.
• Largest source of uncertainty and its improvement. The cell's e.m.f. and internal resistance change while current is drawn: it runs down and warms, so later readings lie on a slightly different line. Take the readings quickly, open the switch between them, and repeat the set in reverse order (high current first) to show whether the values drift. Name the physical cause rather than “human error”, which identifies nothing that could be improved. The syllabus says that an improvement that could have been made with the apparatus provided will not normally gain credit, so “use a digital meter” is not an improvement when the meters are already digital.
• Interleave with the chapters that use this one. Topic 19 (capacitance) puts capacitors into these circuits and reuses Kirchhoff's laws: when you reach it, re-derive the series and parallel resistor formulas and compare them with the capacitor ones. Topic 21 (alternating currents) reuses P = I2R and the diode in circuits. Every Paper 3 electrical experiment uses the meter placements of 10.1.2. 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 10 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 Paper 1 item on this topic can turn on a single step: reading which components are in series or in parallel, inverting 1/R, or deciding which way an output p.d. moves when a sensor warms. A Paper 2 structured question asks you to define e.m.f., explain the difference between e.m.f. and p.d. in terms of energy, state Kirchhoff's laws with the conservation law behind each, show that the series or parallel formula follows from them, and explain why a potentiometer at balance measures an e.m.f.
• Calculations of terminal p.d. and lost volts from E = I(R + r); r and E from two readings or from a V–I graph; combined resistances; currents in a network from Kirchhoff's laws, including two simultaneous equations; divider outputs with and without a load; an e.m.f. from two balance lengths. Only the series and parallel resistor formulas are printed on the Data and formulas sheet; E = W/Q, V = E − Ir, both of Kirchhoff's laws, the divider equation and the potentiometer ratio must be recalled.
• Vary the current with a rheostat, measure the terminal p.d. with a voltmeter across the cell, plot V against I: gradient −r, intercept E. The largest uncertainty is drift: the cell's e.m.f. and internal resistance change while it supplies current. Paper 5 may give the same circuit with fixed resistors and ask for 1/I against R with error bars and a worst acceptable line. Potentiometer and I–V circuits use the same meter placements.
• 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.