Describe an experiment to determine resistance using a voltmeter and an ammeter and do the appropriate calculations

Published by Patrick Mutisya · 8 days ago

Cambridge IGCSE Physics 0625 – 4.2.4 Resistance

Objective

Describe an experiment to determine the resistance of a component using a voltmeter and an ammeter, and perform the required calculations.

Theory

The relationship between voltage (\$V\$), current (\$I\$) and resistance (\$R\$) for an ohmic conductor is given by Ohm’s law:

\$\$

V = I R

\$\$

Re‑arranging gives the expression for resistance:

\$\$

R = \frac{V}{I}

\$\$

By measuring \$V\$ across the component and the current \$I\$ flowing through it, the resistance can be calculated.

Apparatus

  • Resistor (unknown resistance)

  • Digital voltmeter (V)

  • Digital ammeter (A)

  • Adjustable DC power supply

  • Connecting wires with crocodile clips

  • Switch (optional, for safety)

Experimental Circuit

Suggested diagram: Simple series circuit with a power supply, ammeter, resistor, voltmeter (connected in parallel with the resistor), and connecting wires.

Procedure

  1. Connect the circuit as shown in the diagram: the ammeter in series with the resistor, the voltmeter across (parallel to) the resistor.

  2. Set the power supply to a low voltage (e.g., 2 V) and turn it on.

  3. Record the current reading \$I1\$ from the ammeter and the voltage reading \$V1\$ from the voltmeter.

  4. Increase the supply voltage in steps (e.g., 2 V, 4 V, 6 V, 8 V, 10 V). For each step record \$I\$ and \$V\$.

  5. Turn off the power supply and disconnect the circuit.

Data Table

Supply \cdot oltage \$V_{\text{set}}\$ (V)Measured \cdot oltage \$V\$ (V)Measured Current \$I\$ (A)Calculated Resistance \$R = V/I\$ (Ω)
2
4
6
8
10

Calculations

For each row, calculate the resistance using:

\$\$

R = \frac{V}{I}

\$\$

To obtain a single best estimate of the resistance, take the average of the individual \$R\$ values:

\$\$

\overline{R} = \frac{\sum{k=1}^{n} Rk}{n}

\$\$

where \$n\$ is the number of measurements.

Example Calculation

Assume the following recorded values for the 4 V setting:

\$\$

V = 3.96\ \text{V}, \qquad I = 0.020\ \text{A}

\$\$

Then

\$\$

R = \frac{3.96\ \text{V}}{0.020\ \text{A}} = 198\ \Omega

\$\$

If the five calculated resistances are 198 Ω, 200 Ω, 202 Ω, 199 Ω and 201 Ω, the average resistance is

\$\$

\overline{R} = \frac{198 + 200 + 202 + 199 + 201}{5} = 200\ \Omega

\$\$

Sources of Error

  • Internal resistance of the voltmeter and ammeter (affects readings).

  • Contact resistance at the crocodile clips.

  • Temperature change of the resistor during the experiment (resistance may vary with temperature).

  • Reading errors due to limited resolution of the instruments.

Conclusion

By measuring voltage across and current through a component, the resistance can be calculated using Ohm’s law. Repeating the measurement at several voltages and averaging reduces random errors, giving a reliable value for the unknown resistance.