Interactive practical

Resistors in series and parallel

Measure three isolated resistors and four combinations, then compare V–I gradients with series and parallel resistance predictions.

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A-Level Physics

Resistors in series and parallel

CCEA 1210 — matched to your course.

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Practical focus

Measure equivalent resistance for resistor combinations and test the series and parallel relationships.

Practical method

Aim

Verify the rules for combining resistors in series and in parallel by measurement.

Variables

Independent variable: combination of resistors
Dependent variable: total resistance
Control variables: the same resistors; temperature.

Apparatus

Resistors of 10, 22 and 47 Ω
Digital multimeter (ohmmeter)
Ammeter, voltmeter and supply for a check

Method

Measure each resistor individually with the ohmmeter.
Connect combinations in series and in parallel and measure the total resistance.
Calculate expected values: R = R₁ + R₂ + … (series) and \(\dfrac{1}{R}\) = \(\dfrac{1}{R_{1}}\) + \(\dfrac{1}{R_{2}}\) + … (parallel).
Check one combination with the ammeter–voltmeter method.

Sample results

Measured individual values: 10.1, 22.0, 46.8 Ω.

Combination	Predicted / Ω	Measured / Ω
All three in series	78.9	79.0
10 Ω ∥ 22 Ω	6.92	6.94
All three in parallel	6.03	6.04
(10 + 22) ∥ 47	19.0	19.1

Analysis

All measured totals agree with the predictions within 0.5%. The parallel combination of all three (6.04 Ω) is smaller than the smallest resistor, as expected.

Uncertainty

The ohmmeter resolves 0.01 Ω on the 200 Ω range but has a stated accuracy of about ±1%; lead and contact resistance (about 0.1 Ω) matter most for small totals.

Errors and improvements

Problem	Effect	Improvement
Lead and contact resistance	Small totals read high	Short the leads, note the reading and subtract
Using nominal values in predictions	Predictions off by up to the tolerance	Use measured individual values
Loose connections	Fluctuating readings	Use a breadboard or firm clips

Risk assessment

Hazard	Risk	Control measure
Resistors heating in the check circuit	Burns	Keep currents small
Short circuit	Overheating	Check circuits before switching on

Common mistakes

Adding resistances in parallel.
Forgetting to invert \(\dfrac{1}{R}\).
Ignoring lead resistance for small values.

Worked analysis

10.1 Ω ∥ 22.0 Ω: \(\dfrac{1}{R}\) = \(\dfrac{1}{10.1}\) + \(\dfrac{1}{22.0}\) = 0.0990 + 0.0455 = 0.1445, so R = 6.92 Ω (measured 6.94 Ω).

Common misconception

Adding a resistor in parallel always decreases the total resistance, because it adds another path for current.

Assessment coverage

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