Physics 9702 · Paper 2

Resistance & Ohm's Law

tells you how many volts are needed to drive each ampere of current. A big resistance means even a large p.d. gives only a small current.

Defining resistance

R = \frac{V}{I}

Symbols

$R$ = resistance (\Omega)
$V$ = p.d. across the component (V)
$I$ = current in the component (A)

The unit is the (Ω). The definition to quote: one ohm is the resistance when a p.d. of 1 V drives a current of 1 A.
This equation is a definition. It works for every component, at every moment — even for components whose resistance keeps changing.

Worked example

Resistance from meter readings

The ammeter reads 2.4 A and the voltmeter reads 6.0 V. Find the resistance of the component.

$R = \dfrac{V}{I} = \dfrac{6.0}{2.4} = 2.5$ Ω.

Answer

R = 2.5 \ \Omega

The measuring circuit

To measure R you need both meter readings at once. The ammeter goes in series with the component, so the same current passes through both.
The voltmeter goes in parallel, across the component, so it reads the p.d. between the component's two ends.

A lab bench: a power supply connected to a thin test wire held between two clamp stands, with an ammeter and a voltmeter. — The real bench for measuring resistance: the power supply drives a current through the test wire; the ammeter (in series) reads that current, and the voltmeter (in parallel, across the wire) reads the p.d. Then R = V / I.

To measure resistance: the ammeter sits in series (same current), the voltmeter sits in parallel across the component (same p.d.). Then R = V / I.

Your turn— tap to reveal the worked answer (9702-style)

A student puts the voltmeter in series with the lamp instead of across it. What happens?

Answer: a voltmeter has a very large resistance, so putting it in series almost stops the current. The lamp goes out and neither reading is useful. Ammeter in series, voltmeter across: that order never changes. (9702-style)

Ohm's law, said precisely

For a metal wire at steady temperature, something extra is true: double the p.d. and the current doubles. I is directly proportional to V.
That statement is : the current in a conductor is directly proportional to the p.d. across it, provided its temperature stays constant. The condition earns a mark of its own, so say it. A component that obeys the law is called ohmic.
Careful: $R = V/I$ is not Ohm's law. The equation defines R for anything. Ohm's law is the extra claim that R stays constant, and it is true only for some components.

$R = V/I$ always works: it is a definition. Ohm's law is the special claim that I ∝ V, true for a metal at constant temperature and false for a lamp or a diode.

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