Physics · Lesson 33

Practical 6: Ohm’s law, resistivity, potentiometer and metre bridge

WAECNECO

What the syllabus asks

WAEC: Ohm’s law; resistance and resistivity of a wire; potentiometer (comparison of e.m.f.s, internal resistance of a cell); metre bridge (unknown resistance). Links to p-units on current electricity.

NECO: Ohm’s law; resistance and resistivity of a wire; potentiometer (comparison of e.m.f.s, internal resistance of a cell); metre bridge (unknown resistance). Links to p-units on current electricity.

What you will learn

Verify Ohm’s law and find a resistance from a V–I graph.
Determine the resistivity of a wire.
Explain the potentiometer principle and compare e.m.f.s.
Determine the internal resistance of a cell with a potentiometer.
Determine an unknown resistance with a metre bridge.
Linearise electrical formulae and deduce constants from graphs.
State precautions and sources of error in electrical experiments.
Answer part (b) items on e.m.f., resistivity and resistor networks.

Key points

V against I: slope R.
R against l: slope ρ/A; sample ρ = 5.00 × 10⁻⁷ Ω m (constantan).
Potentiometer: no current at balance; E ∝ l.
1/l against 1/R: r = slope ÷ intercept; sample r = 0.99 Ω.
Metre bridge: X/R = l/(100 − l); sample X = 4.00 Ω.
Intercept of 1/l against R = 0.0100 cm⁻¹ checks the wire.
Tap the jockey; keep balance near the middle.
Open the key between readings.
Convert units before squaring.
Draw the circuit with standard symbols.

Start here: Concept summary: the electricity practicals

Electricity questions are the third pillar of the WAEC and NECO physics practical, alongside mechanics and light. The apparatus is a cell or accumulator, a key, a rheostat, an ammeter, a voltmeter or galvanometer, a length of resistance wire stretched along a metre rule, a jockey, connecting wires and a resistance box. Four experiments account for most questions:

Ohm’s law for a resistor: V against I is a straight line through the origin, with slope R.
Resistance of a wire and resistivity: R against length l is a straight line with slope ρ/A.
Potentiometer: comparing e.m.f.s or finding the internal resistance of a cell from balance lengths.
Metre bridge (a form of the Wheatstone bridge): finding an unknown resistance from the balance point.

The potentiometer and metre bridge are null methods: you look for the position of the jockey where the galvanometer shows zero deflection. Null methods are accurate because at balance no current flows through the galvanometer branch, so the meter’s own resistance and calibration do not matter; you only need a uniform wire and a metre rule.

Before connecting anything, draw the circuit diagram neatly with standard symbols (many questions award marks for it) and check it against the apparatus. Then connect, leaving the key open. Close the key only when taking readings. Electrical apparatus in school laboratories is often worn: dirty terminals, loose crocodile clips and kinked wires are the main cause of unsteady readings. Clean and tighten every joint before you start.

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Practice questions

1. V / V = 0.60, 1.20, 1.85, 2.40 for I / A = 0.10, 0.20, 0.30, 0.40. Estimate R.

Show worked answer

The ratios are about 6.0 Ω; from a graph slope ≈ (2.40 − 0.60)/(0.40 − 0.10) = 6.0 Ω.

2. State Ohm’s law with its condition.

Show worked answer

The current through a metallic conductor is directly proportional to the p.d. across it, provided temperature and other physical conditions remain constant.

3. A wire 0.80 m long has R = 3.2 Ω and diameter 0.40 mm. Find ρ.

Show worked answer

A = 1.26 × 10⁻⁷ m²; ρ = RA/l = 3.2 × 1.26 × 10⁻⁷/0.80 = 5.04 × 10⁻⁷ Ω m.

4. Why should the key be opened between readings in resistance experiments?

Show worked answer

To prevent the current heating the wire (which changes its resistance) and to avoid running down the cell.

5. A potentiometer balances at 72.0 cm for a cell on open circuit and 60.0 cm when a 5.0 Ω resistor is connected across it. Find r.

Show worked answer

r = R(l₀/l − 1) = 5.0 × (72.0/60.0 − 1) = 1.0 Ω.

Key words

Ohm’s law: I ∝ V for a metallic conductor at constant temperature.
Resistivity: ρ = RA/l; property of the material; Ω m.
E.m.f.: Energy converted per unit charge; open-circuit p.d.
Internal resistance: Resistance inside a cell.
Terminal p.d.: P.d. across a cell’s terminals while it delivers current.
Potentiometer: Uniform wire used to compare p.d.s by a null method.
Jockey: Sliding contact tapped onto a bridge or potentiometer wire.
Galvanometer: Sensitive meter showing small currents and their direction.
Balance point: Position of zero galvanometer deflection.
Metre bridge: Wheatstone bridge using a 100 cm wire.
Rheostat: Variable resistor used to control current.
Null method: Measurement taken when a detector reads zero.

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