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The AQA A-Level Physics specification includes several required practicals related to electricity. This lesson covers the three main electricity practicals: determining EMF and internal resistance, measuring resistivity, and investigating I-V characteristics. For each practical, we cover the method, apparatus, analysis, and common sources of error.
Spec mapping: This lesson maps to AQA 7408 specification sections 3.5.1.4 — Resistivity (Required Practical 5) and 3.5.1.6 — EMF and internal resistance (Required Practical 6), together with the I–V characteristics practical that supports section 3.5.1.3. The Required Practicals are formally examined in the written papers (an extended-response practical question typically appears on each electricity paper) and contribute to the practical-skills endorsement (CPAC criteria 1–5). (Refer to the official AQA specification document for exact wording.)
Synoptic links:
- 3.1 — Measurements and their errors: the entire framework of random and systematic uncertainty, percentage uncertainty propagation, and graph-based analysis (intercepts, gradients, lines of best fit) developed in the opening unit of the spec is applied in this lesson. Required Practicals are the operational instantiation of the measurement-theory content.
- 3.5.1.4 — Resistivity: Required Practical 5 is the experimental determination of the material property introduced theoretically in Lesson 5. The R = ρL/A equation becomes a measurement procedure here.
- 3.5.1.6 — EMF and internal resistance: Required Practical 6 is the experimental determination of ε and r introduced theoretically in Lesson 7. The V = ε − Ir equation becomes a graph-fitting procedure here.
To determine the EMF (ε) and internal resistance (r) of a cell by measuring terminal p.d. and current for different external resistances.
The cell is connected in series with the ammeter and the variable resistor. The voltmeter is connected in parallel across the cell (measuring terminal p.d.). A switch is included so current only flows when readings are taken (to avoid draining the cell and to minimise heating effects).
Plot a graph of V (y-axis) against I (x-axis).
From V = ε − Ir:
A student obtains the following data:
| I (A) | V (V) |
|---|---|
| 0.10 | 1.43 |
| 0.20 | 1.37 |
| 0.30 | 1.30 |
| 0.40 | 1.23 |
| 0.50 | 1.17 |
| 0.60 | 1.10 |
From the graph (V vs I), the line of best fit gives:
Verification: At I = 0.30 A: V = 1.50 − 0.67 × 0.30 = 1.50 − 0.20 = 1.30 V ✓
| Source of error | Effect | Improvement |
|---|---|---|
| Cell draining during experiment | ε decreases, readings inconsistent | Open switch between readings; work quickly |
| Heating of components | Resistance changes with temperature | Allow cooling time; use low currents |
| Contact resistance | Adds to measured internal resistance | Use clean, tight connections |
| Voltmeter draws current | Measured V slightly low; calculated ε slightly low | Use a high-resistance voltmeter (digital) |
| Parallax error (analogue meters) | Random error in readings | Read at eye level, perpendicular to scale |
Exam Tip: When asked to describe this experiment, always state what you measure, what you plot, and how you obtain ε and r from the graph. A common exam error is to describe the method but forget the analysis.
To determine the resistivity of a metal wire by measuring its resistance at different lengths.
The wire under test is stretched alongside a metre ruler. One crocodile clip is fixed at one end. The other is moved to different positions along the wire to vary the length. An ammeter is in series with the wire and power supply. A voltmeter is connected across the section of wire being tested (between the two crocodile clips).
Plot a graph of R (y-axis) against L (x-axis).
From R = ρL/A:
A student measures the diameter of a nichrome wire at five positions:
| Reading | Diameter (mm) |
|---|---|
| 1 | 0.26 |
| 2 | 0.27 |
| 3 | 0.26 |
| 4 | 0.25 |
| 5 | 0.26 |
Mean diameter = (0.26 + 0.27 + 0.26 + 0.25 + 0.26)/5 = 1.30/5 = 0.260 mm = 2.60 × 10⁻⁴ m
Radius = 1.30 × 10⁻⁴ m
Area = π × (1.30 × 10⁻⁴)² = π × 1.69 × 10⁻⁸ = 5.31 × 10⁻⁸ m²
The student's R vs L graph has a gradient of 19.8 Ω m⁻¹.
ρ = gradient × A = 19.8 × 5.31 × 10⁻⁸ = 1.05 × 10⁻⁶ Ω m
The accepted value for nichrome is approximately 1.10 × 10⁻⁶ Ω m, so this result is within 5% — good agreement.
The range in diameter readings is 0.27 − 0.25 = 0.02 mm.
Half-range = 0.01 mm.
Percentage uncertainty in d = (0.01/0.26) × 100 = 3.8%
Since A = πd²/4, the percentage uncertainty in A is 2 × 3.8% = 7.7% (because d is squared).
| Source of error | Effect | Improvement |
|---|---|---|
| Wire not uniform | Area varies along length | Measure diameter at many points; calculate mean |
| Wire heating up | R increases, not just due to length | Use low current; take readings quickly |
| Kinks in wire | Effective length uncertain | Straighten wire carefully (do not stretch it) |
| Measuring from wrong point | Systematic error in L | Measure from inside edges of crocodile clips |
| Zero error on micrometer | Systematic error in diameter | Check and record zero error; correct readings |
Exam Tip: The biggest source of uncertainty is usually the diameter measurement because it is small and is squared in the area calculation. Always emphasise this in uncertainty discussions. Take multiple measurements at different positions AND different orientations (rotate the wire 90° between readings).
To investigate the I-V characteristics of a filament lamp, a diode, and a resistor.
The component is connected in series with an ammeter and the variable power supply. A voltmeter is connected in parallel across the component. To obtain readings at both positive and negative voltages (necessary for the diode characteristic), the connections to the power supply are reversed.
| Component | I-V Graph Shape | Explanation |
|---|---|---|
| Fixed resistor | Straight line through origin | Ohmic: R constant, V ∝ I |
| Filament lamp | S-shaped curve through origin (symmetric) | R increases with temperature; less current per extra volt |
| Diode | Forward: steep curve above ~0.7 V; Reverse: ≈ 0 | One-way conduction; threshold voltage needed |
A student records the following data for a filament lamp:
| V (V) | I (A) | R = V/I (Ω) |
|---|---|---|
| 0.50 | 0.42 | 1.19 |
| 1.00 | 0.55 | 1.82 |
| 2.00 | 0.72 | 2.78 |
| 4.00 | 0.93 | 4.30 |
| 6.00 | 1.08 | 5.56 |
| 8.00 | 1.20 | 6.67 |
| 10.00 | 1.30 | 7.69 |
| 12.00 | 1.38 | 8.70 |
The resistance increases from 1.19 Ω at 0.5 V to 8.70 Ω at 12 V — a factor of about 7. This is because the filament temperature increases from near room temperature to about 2500°C, dramatically increasing the rate of lattice ion scattering.
For the diode: The current increases very rapidly above the threshold voltage. Use a protective resistor (e.g., 100 Ω) in series to limit the current and prevent damage.
For the filament lamp: Take readings quickly at each voltage to minimise the effect of the filament reaching thermal equilibrium at different rates.
For the resistor: Keep the current low to prevent heating, which would make the results non-ohmic.
| Source of error | Effect | Improvement |
|---|---|---|
| Component heating | Resistance changes during measurement | Take readings quickly; allow cooling between sets |
| Ammeter resistance | Measured V is slightly different from true V across component | Use ammeter with very low resistance |
| Voltmeter draws current | Ammeter reads slightly more than component current | Use voltmeter with very high resistance |
| Insufficient data points | Graph shape unclear | Take many readings, especially near regions of rapid change |
| Not reversing connections | Only half the characteristic plotted | Reverse supply connections systematically |
When calculating resistance from R = V/I:
Percentage uncertainty in R = percentage uncertainty in V + percentage uncertainty in I
When calculating resistivity from ρ = RA/L:
Percentage uncertainty in ρ = % uncertainty in R + % uncertainty in A + % uncertainty in L
And since A = πd²/4:
Percentage uncertainty in A = 2 × percentage uncertainty in d
A student measures V = 4.2 ± 0.1 V and I = 0.35 ± 0.01 A. Calculate R and its absolute uncertainty.
Solution:
R = V/I = 4.2/0.35 = 12.0 Ω
% uncertainty in V = (0.1/4.2) × 100 = 2.4%
% uncertainty in I = (0.01/0.35) × 100 = 2.9%
% uncertainty in R = 2.4 + 2.9 = 5.3%
Absolute uncertainty in R = 5.3% × 12.0 = ±0.6 Ω
R = 12.0 ± 0.6 Ω
Percentage difference=accepted value∣experimental value−accepted value∣×100%
A student measures the resistivity of copper as 1.80 × 10⁻⁸ Ω m. The accepted value is 1.68 × 10⁻⁸ Ω m.
Solution:
Percentage difference = |1.80 − 1.68| / 1.68 × 100% = 0.12/1.68 × 100% = 7.1%
If the total experimental uncertainty is greater than 7.1%, the result is consistent with the accepted value. If the uncertainty is less than 7.1%, there may be a systematic error.
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