Resistance R = V/I (Ω): the definition
Resistance = the ratio of the p.d. across a component to the current through it: ; unit ohm (Ω). Full marks need both (1) ratio of p.d. to current and (2) the unit Ω. Rearrange as or . Ohm's law: for a metal conductor at constant temperature , so is constant. One ohm = one volt per ampere (1 Ω = 1 V/A). Mini-example: 6.0 V driving 0.40 A → Ω.
Four factors set a wire's resistance
Wire resistance depends on four things: length ( — double the length, double ); cross-sectional area ( — a thicker wire has LOWER resistance, more electrons flow in parallel); material (resistivity ρ, unit Ω·m — copper low, nichrome high); temperature (a metal's rises as it heats: more lattice vibration → more electron collisions; an NTC thermistor does the opposite). The full comparison table is in the note.
Measuring resistance: A series, V parallel
Standard practical: a variable resistor to change the current, an ammeter in series to read current (A), and a voltmeter in parallel across the component to read p.d. (V). Compute for each pair. To test length, clip a resistance wire at different points and plot against (a straight line through the origin confirms ). Keep the current low so the wire does not heat, and keep other dimensions constant when varying one factor.
Drawn from real examiner reports.
Thicker wire = more resistance (wrong)
A common error: "a thicker wire has more resistance because there is more material." Wrong. A larger cross-sectional area lets MORE electrons flow at once — like extra motorway lanes — so resistance is LOWER: . A wider pipe passes more water for the same pressure; a thicker wire passes more current for the same p.d., which by means lower resistance.
June 2024 Paper 1P Q11(b)(ii) — the examiner specifically highlighted that candidates confused the effect of wire dimensions on resistance, applying an incorrect "more material = more resistance" logic instead of the correct inverse relationship with cross-sectional area.
Longer cable slows electrons (wrong)
A longer cable does not slow the electrons by making them "travel further". The correct chain: (1) a longer wire has more resistance (); (2) for the same e.m.f., more resistance means less current (); (3) so the charging current falls. The electrons' drift speed barely changes — it is the current that drops. State both the resistance AND current change.
June 2024 Paper 1P Q11(b)(ii): "Many [candidates] thought that a longer cable would cause electrons to take more time to travel — basing their argument on speed = distance/time and electrons travelling at a constant speed." Paraphrased from the published examiner report.
Resistance is not "opposition to current"
Everyday phrasing like "opposition to current" is not accepted. The mark scheme wants the ratio: "the p.d. across a component divided by the current through it", , plus the unit ohm (Ω). Two elements for full marks: (1) ratio of p.d. to current, (2) unit Ω. Dropping the unit is an avoidable one-mark loss the examiner report specifically flags.
November 2024 Paper 1P examiner summary: "Recall the units given in the specification and use them appropriately, for instance resistance." — unit (Ω) is frequently omitted in resistance definition answers.
Metal vs NTC thermistor with heat
The two respond to heat in OPPOSITE ways. A metal wire: resistance INCREASES as temperature rises (lattice ions vibrate more → more electron collisions). An NTC thermistor (negative temperature coefficient): resistance DECREASES (more charge carriers are released). Do not assume every component behaves like a metal — check which one the question names.
Scale resistance, do not add lengths
When length or area changes, scale by a ratio — do not add or subtract. For a 30 cm wire of 4.5 Ω, a 90 cm wire is Ω (three times), NOT or . For area, halving A doubles R (). Combine both as multiplying factors, e.g. three times longer and half the area gives ×3 × 2 = ×6.
Voltmeter in series (wrong reading)
In a resistance circuit the ammeter goes in series and the voltmeter in parallel across the component. Putting the voltmeter in series adds its high resistance and gives a tiny, misleading reading; putting the ammeter in parallel nearly short-circuits the component. Weaker candidates lose the mark by drawing the voltmeter in the main line, not across the component.
Effect-on-current: two-step chain
For "a wire is longer/thinner/hotter — explain the effect on current", give two steps: (1) state what happens to R (e.g. "longer → more resistance"); (2) link to current by ("for the same p.d., more R → less current"). Skipping step (1) loses the linkage mark.
Always write the unit Ω
Resistance answers must carry the unit ohm (Ω); the examiner report flags dropped units as an easy lost mark. After any calculation, write the number AND Ω. The same discipline applies to V (volts) and I (amperes) — never leave a bare number.
Use the ratio method for changes
When only the wire's dimensions change (same material), use . Read each ratio, multiply, then scale the original R. This handles length and area in one line. Sense-check: a longer or thinner wire → higher R.
Name the unknown, then rearrange V = IR
Before substituting, identify the unknown, then pick the right form: , or . Finding p.d.? multiply; finding current or resistance? divide. Check the units follow (A × Ω = V). A wrong rearrangement is the commonest Ohm's-law slip.
| Quantity | Symbol | Formula | Unit |
|---|---|---|---|
| Resistance | ohm (Ω) | ||
| Potential difference | volt (V) | ||
| Current | ampere (A) |
Where: = potential difference (p.d.) in volts (V), = current in amperes (A), = resistance in ohms (Ω).
Factors affecting resistance of a wire:
| Factor | Relationship | Direction | Reason |
|---|---|---|---|
| Length | Longer → more | More collisions along longer path | |
| Cross-sectional area | Thicker → less | More electrons pass in parallel | |
| Material | depends on resistivity | Copper low; nichrome high | Resistivity is a property of the material |
| Temperature | Metal: increases with | Hotter → more | More lattice vibration → more collisions |
Define resistance.
A resistor has a potential difference (p.d.) of 9.0 V across it and a current of 0.30 A flowing through it.
(a) Calculate the resistance of the resistor. [2]
(b) The same p.d. is maintained but the current increases to 0.45 A. Calculate the new resistance. [1]
