At a glance
- Cambridge 9702
- AS topics 9 and 10
- Edexcel IAL
- Unit 2 WPH12: 1 h 30 min, 80 marks
- Core practicals
- IAL CP7 (resistivity), CP8 (e.m.f. and internal resistance)
- Key equations
- R = ρL/A; E = I(R + r); V = IR
Where electricity sits in each specification
| Board and unit | Content |
|---|---|
| Cambridge 9702 topic 9 (AS) | Electric current and charge, I = Anvq, potential difference and power, resistance, I-V characteristics, resistivity, thermistors and LDRs |
| Cambridge 9702 topic 10 (AS) | Circuit symbols, e.m.f. and internal resistance, Kirchhoff's first and second laws, series and parallel resistors, potential dividers, potentiometers and null methods |
| Edexcel IAL Unit 2 (WPH12) | Current, V = W/Q, resistance and Ohm's law, combining resistors, P = VI, I-V graphs, resistivity and Core Practical 7, I = nqvA, potential along a wire, potential dividers, e.m.f., internal resistance and Core Practical 8, thermistors and LDRs |
Capacitors are A Level in both: Cambridge 9702 topic 19 and Edexcel IAL Unit 4 (Core Practical 11).
The key ideas
Current is the rate of flow of charge and is conserved at a junction (Kirchhoff's first law, a consequence of conservation of charge). Around any closed loop, the sum of e.m.f.s equals the sum of p.d.s (Kirchhoff's second law, conservation of energy). Resistors in series add, R = R1 + R2; in parallel, 1/R = 1/R1 + 1/R2, so the total is less than the smallest resistor.
E.m.f. is the energy transferred to electrical energy per unit charge by the source; p.d. is the energy transferred from electrical energy per unit charge by a component. A real cell has internal resistance r, so some energy is dissipated inside it and the terminal p.d. V = E - Ir falls as current increases. Plotting V against I gives a straight line with gradient -r and intercept E, which is Edexcel Core Practical 8.
A potential divider splits a supply in proportion to resistance: Vout = Vin × R2/(R1 + R2). A thermistor (NTC) has lower resistance when hotter; an LDR has lower resistance in brighter light. Placed in a divider, they give an output that depends on temperature or light. Resistivity is a property of the material: ρ = RA/L.
Worked example 1: internal resistance
- A cell of e.m.f. 6.0 V and internal resistance 0.50 Ω is connected to a 2.5 Ω resistor.
- Total resistance = 2.5 + 0.50 = 3.0 Ω, so I = 6.0 ÷ 3.0 = 2.0 A.
- Terminal p.d. = IR = 2.0 × 2.5 = 5.0 V.
- Lost volts = Ir = 2.0 × 0.50 = 1.0 V, and 5.0 + 1.0 = 6.0 V, matching the e.m.f.
Worked example 2: a thermistor in a potential divider
- A 9.0 V supply is connected across a 2.0 kΩ fixed resistor in series with a thermistor. The output is taken across the thermistor.
- When the thermistor is 4.0 kΩ: Vout = 9.0 × 4.0/(2.0 + 4.0) = 6.0 V.
- When it warms and falls to 1.0 kΩ: Vout = 9.0 × 1.0/(2.0 + 1.0) = 3.0 V.
- So the output across the thermistor falls as temperature rises. To make the output rise with temperature, take it across the fixed resistor instead.
Worked example 3: resistivity of a wire
- A wire 1.50 m long and 0.40 mm in diameter has resistance 12.0 Ω.
- A = π × (0.20 × 10^-3)^2 = 1.26 × 10^-7 m^2.
- ρ = RA/L = 12.0 × 1.26 × 10^-7 ÷ 1.50 = 1.01 × 10^-6 Ω m, close to the value for nichrome.
Common mistakes that cost marks
- Using e.m.f. and p.d. as if they mean the same thing.
- Calculating cross-sectional area with the diameter instead of the radius, or in mm^2.
- Adding parallel resistances directly.
- Forgetting to take the reciprocal at the end of a parallel calculation.
- Saying a thermistor's resistance always falls with temperature without stating it is an NTC thermistor.
- Writing Ω m for resistance or Ω for resistivity.
Exam technique and how a tutor helps
Redraw complicated circuits in a simpler form, mark currents at each junction, and apply Kirchhoff's laws one loop at a time. For potential divider questions, decide first which resistor the output is across, then reason about what happens when one resistance changes. Explanations score best as a chain: temperature rises, resistance of thermistor falls, share of p.d. across it falls, output falls.
Practical questions often ask how to find resistivity from a graph of R against L: the gradient is ρ/A. Know the sources of uncertainty: diameter measured with a micrometer at several places, and contact resistance at the crocodile clips.
In one-to-one lessons a tutor builds the student's circuit reasoning step by step on the shared whiteboard, then sets mixed past-paper questions, where the most common gaps, e.m.f. versus p.d. and divider reasoning, are fixed with targeted practice.
Self-check: can you do these?
- Find the total resistance of 6.0 Ω and 3.0 Ω in parallel. (Answer: 2.0 Ω)
- A charge of 30 C flows in 1 minute. Find the current. (Answer: 0.50 A)
- State Kirchhoff's second law and the conservation law it follows from. (Answer: sum of e.m.f.s = sum of p.d.s round a loop; energy)
- What does the y-intercept of a V-I graph for a cell show? (Answer: the e.m.f.)
- An LDR is darkened. Does its resistance rise or fall? (Answer: rise)
Common questions
Is electricity AS or A Level?
Current electricity and d.c. circuits are AS in both boards: Cambridge 9702 topics 9 and 10, and Edexcel IAL Unit 2. Capacitors, electric fields and electromagnetism come at A Level.
What are the electricity core practicals?
In Edexcel IAL, Core Practical 7 determines the resistivity of a material and Core Practical 8 determines the e.m.f. and internal resistance of a cell. Cambridge 9702 has no named list but often uses circuits in Paper 3 and Paper 5.
Why does terminal p.d. fall when more current is drawn?
Because the p.d. across the internal resistance, Ir, increases with current, leaving less of the e.m.f. across the external circuit.
Do I need the potentiometer?
Cambridge 9702 names the potentiometer and null methods with a galvanometer in topic 10.3. Edexcel IAL focuses on potential dividers and the potential along a uniform wire.
How much do LiveTutor A-Level Physics lessons cost?
Every lesson is one to one, online and 60 minutes, at one flat rate of $15 a lesson for every subject and level. Families choose a weekly plan of 1 to 5 lessons billed monthly, and the first lesson is a free trial.
Sources
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