CIE iGCSE Co-ordinated Sciences-P4.2.4 Resistance- Study Notes- New Syllabus

Aim

To determine the resistance of a given resistor using measurements of potential difference (V) and current (I).

Apparatus

• Resistor under test (unknown R)
• Variable dc supply (0–12 V) or a power supply with rheostat
• Ammeter (suitable range, e.g. 0–1 A) — connected in series
• Voltmeter (suitable range, e.g. 0–10 V or 0–20 V) — connected in parallel across the resistor
• Connecting leads, switch, low-resistance rheostat (optional)
• Meter selection tool (set ranges) and notebook for data

Circuit and Connections (important)

• Connect the ammeter in series with the resistor and supply so the whole circuit current flows through the ammeter.
• Connect the voltmeter in parallel with the resistor only (not across the supply unless measuring source voltage intentionally).
• Polarity: connect the positive terminal of voltmeter to the resistor end connected to the positive supply terminal; ammeter polarity likewise (or use the meter’s markings).
• Use a switch or rheostat to vary the voltage and therefore the current.

Procedure (step-by-step)

1. Check meter ranges: start with the highest range for safety (ammeter high range, voltmeter high range).
2. Set up the circuit as above. Close switch with supply set to zero volts.
3. Increase supply to a small non-zero voltage (e.g. 1.0 V). Wait until readings stabilise. Record V (voltmeter) and I (ammeter).
4. Increase supply in steps (e.g. 1.0 V → 2.0 V → 3.0 V …) up to a safe maximum (do not exceed resistor power rating). Record several pairs of V and I (at least 5 different readings over a useful range).
5. If readings are too small or too large, change the meter range and repeat the measurement for that step (note the range used).
6. Take multiple readings at each step and average them if possible to reduce random error.
7. Use the data to calculate resistance by: (a) Single-reading method: \(\;R = \dfrac{V}{I}\) for each pair (take mean). (b) Graph method (recommended): plot V (vertical axis) against I (horizontal axis) and determine the slope \(\dfrac{\Delta V}{\Delta I}\) — slope = R.

Data Table (example format)

Worked Example — Single-reading method (step-by-step arithmetic)

Suppose at one step you measured: \(V = 5.00\ \text{V}\) and \(I = 0.50\ \text{A}\).

Use the resistance formula \(\displaystyle R = \frac{V}{I}\).

Compute carefully, digit by digit:

• \(V = 5.00\ \text{V}\)
• \(I = 0.50\ \text{A}\)
• \(\displaystyle R = \frac{5.00}{0.50}.\) Divide 5.00 by 0.50: \(0.50 \times 10 = 5.0\), therefore \(5.00 \div 0.50 = 10.0.\)
• \(\boxed{R = 10.0\ \Omega}\)

Worked Example — Graph (more accurate)

• Plot V (y axis) against I (x axis) using the table data points.
• If the resistor is ohmic, points should lie on a straight line through the origin.
• Pick two well-separated points on the best-fit line, e.g. (I₁ = 0.10 A, V₁ = 1.0 V) and (I₂ = 0.50 A, V₂ = 5.0 V).
• Compute slope = ΔV / ΔI = (V₂ − V₁) / (I₂ − I₁) = (5.0 − 1.0) V / (0.50 − 0.10) A = 4.0 V / 0.40 A.
• Compute: \(4.0 \div 0.40 = 10.0\). So \(\boxed{R = 10.0\ \Omega}\).

Why the graph method is better

• Reduces random errors in individual readings.
• Using slope averages many measurements → more reliable estimate of R.
• Deviations from straight line reveal non-ohmic behaviour or experimental error.

Precautions & Practical Tips

• Always connect the ammeter in series and the voltmeter in parallel (incorrect connection can damage meters).
• Start with high ranges on meters; then reduce for better accuracy if safe.
• Do not exceed the resistor’s power rating: check \(P = V \times I\) for each reading. If \(P\) approaches or exceeds the resistor rating, stop or reduce voltage.
• Allow readings to stabilise before recording (wait a few seconds for meters to settle).
• Take several readings over a range of voltages. Avoid using only one reading—use at least 4–6 points for a good V–I graph.

How to report the result

• State measured resistance with appropriate units and significant figures, e.g. \(R = 10.0\ \Omega\).
• If using multiple readings, give average and a simple uncertainty (e.g. standard deviation or range), e.g. \(R = 10.0 \pm 0.2\ \Omega\).