The big idea: Push current through a thin, poor wire and only a trickle gets through; a fat copper one lets it flow freely. How hard a component makes it to push current through is its resistance.
Resistance in numbers: A bigger resistance needs a bigger voltage (the push) for the same current.
Resistance is voltage ÷ current, and its unit is the ohm (Ω).
Measuring resistance: the ammeter (A) reads the current I through R; the voltmeter (V) reads the voltage across R. Then R = V ÷ I.
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Spot it: More resistance → less current for the same voltage.
To find a component's resistance you measure the voltage across it (with a voltmeter) and the current through it (with an ammeter), then divide.
Where resistance comes from
The heating effect: Every collision hands energy from the electrons to the lattice, so a current always heats a resistor. Kept at a constant temperature, a metal wire has a constant resistance: it is ohmic.
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The definition of resistance links the three quantities. The voltage across a component equals the current through it times its resistance:
- potential difference / voltage (V)
- current (A)
- resistance (Ω, ohms)
Ohm's law, exactly: Ohm's law: the current in a metal conductor is proportional to the pd across it, provided its temperature stays constant.
R = V ÷ I works for any component at any moment; only an ohmic one keeps the same R as V changes.
V = I R. Cover the one you want: two letters side by side → multiply (V = I R); one above the other → divide (R = V ÷ I, or I = V ÷ R).
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Reading the I–V graph: An I–V graph plots current against voltage.
For a fixed resistance the points lie on a straight line through the origin, and R = V ÷ I is the same at every point on it.
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A resistor's current–voltage graph is a straight line through the origin. At a voltage of 6.0 V the current is 1.5 A. Find its resistance.
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Resistivity
- resistivity (Ω m)
- cross-sectional area (m²)
- length (m)
How R scales: R = ρL/A: twice the length, twice the resistance; twice the area, half the resistance. For a round wire A = πd²/4, so R ∝ L/d²: half the diameter means four times the resistance.
Reshape a fixed volume of metal to 4 times the length and its area falls to a quarter: R rises 4 × 4 = 16 times.
A copper wire is 3.0 m long with a diameter of 0.50 mm. The resistivity of copper is 1.7 × 10⁻⁸ Ω m. Calculate its resistance.
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How this is tested — resistance and Ohm's law are the backbone of the circuit questions:
Paper 1A
- Read a resistance off an I–V graph (R = V ÷ I at a point).
- Decide whether a component is ohmic or non-ohmic.
Paper 2
- Use R = ρL/A to see how resistance changes when a wire's length or thickness changes.
The classic trap: Thinking a curved I–V graph means 'no resistance' — it just means the resistance changes (non-ohmic).
Ohmic vs non-ohmic: Ohmic = obeys Ohm's law: a straight I–V line through the origin, so R stays constant (e.g. a fixed resistor at steady temperature).
Non-ohmic = a curved I–V graph, so R changes with the current (e.g. a filament lamp, whose resistance rises as it heats up).
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The words to know
| Word | What it means |
|---|---|
| Resistance | pd across a component ÷ current through it (R = V/I), in ohms |
| Ohm's law | I ∝ V for a metal conductor at constant temperature |
| Ohmic | Obeys Ohm's law: a straight I–V line through the origin |
| Resistivity | ρ = RA/L, a property of the material, in Ω m |
Component P has a straight I–V line through the origin; component Q is a filament lamp with a curved I–V graph. (a) State, with a reason, which component is ohmic. (b) Outline how the resistance of Q changes as the current through it increases.
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