Charge, current, potential difference and resistivity
This topic sets up the definitions every later circuit question depends on. Resistivity then explains why a long thin wire has a bigger resistance than a short thick one of the same metal.
Part 1 of 3: Learn it
In short
- I = ΔQ ÷ Δt; V = W ÷ Q; R = V ÷ I.
- Resistivity ρ = RA ÷ L, measured in Ω m, is a property of the material.
- A superconductor has zero resistivity below its critical temperature.
Where this is in your specification
Spec points: AQA 7408 3.5.1.1 to 3.5.1.3 (required practical 5), OCR A H556 4.1 and 4.2, Edexcel 9PH0 Topic 3
| Board | Topic: Electricity |
|---|---|
| AQA 7408 | 3.5 |
| Edexcel 9PH0 | Topic 3 |
| OCR H556 | 4.1 to 4.3 |
| Higher C857 76 | Electricity: monitoring and measuring AC, current, potential difference, power and resistance, electrical sources and internal resistance, semiconductors |
The definitions
| Quantity | Definition | Unit |
|---|---|---|
| Current I | rate of flow of charge, ΔQ ÷ Δt | ampere (A), 1 C per second |
| Potential difference V | work done per unit charge, W ÷ Q | volt (V), 1 J per coulomb |
| Resistance R | V ÷ I | ohm (Ω), 1 V per ampere |
Charge comes in multiples of the electron charge, e = 1.60 × 10⁻¹⁹ C. Dividing a current by e gives the number of electrons passing a point each second.
I-V characteristics
- Ohmic conductor (at constant temperature): a straight line through the origin, so R is constant.
- Filament lamp: a curve that flattens, because the filament heats up and its resistance rises.
- Semiconductor diode: almost no current in reverse; in the forward direction, current flows once the p.d. passes about 0.6 V.
Resistivity
R is resistance, A the cross-sectional area and L the length. For a wire of diameter d, A = πd²/4. In the required practical, measure the diameter with a micrometer in several places, find R for several lengths, and use the gradient of R against L, which equals ρ/A.
For metals, resistivity rises with temperature. For a thermistor (NTC), resistance falls as temperature rises.
Superconductivity
Some materials have exactly zero resistivity when cooled below a critical temperature. Uses include very strong electromagnets, such as in MRI scanners and particle accelerators, and power cables with no heating losses.
What is the unit of resistivity?
Show the answer
Ω m (ohm metre).
Part 2 of 3: See it worked
Worked examples
Example 1
A copper wire is 2.0 m long with a diameter of 0.50 mm. The resistivity of copper is 1.7 × 10⁻⁸ Ω m. Find its resistance.
- A = π × (0.25 × 10⁻³)² = 1.96 × 10⁻⁷ m²
- R = ρL ÷ A = 1.7 × 10⁻⁸ × 2.0 ÷ 1.96 × 10⁻⁷
- R = 0.173 Ω
Answer: 0.17 Ω (2 s.f.).
Example 2
How many electrons pass a point each second when the current is 0.48 A?
- Charge per second = 0.48 C
- Number = 0.48 ÷ (1.60 × 10⁻¹⁹)
Answer: 3.0 × 10¹⁸ electrons.
Common mistakes
- Using the diameter instead of the radius in πr².
- Leaving the diameter in mm when working out the area.
- Taking resistance as the gradient of an I-V graph.
- Saying resistivity depends on the wire's length. Resistance does; resistivity does not.
Define potential difference.
Show the answer
The work done (energy transferred) per unit charge between two points.
Part 3 of 3: Test yourself
Check yourself
Answer each one in your head or on paper first, then open it to check.
What is the unit of resistivity?
Ω m (ohm metre).
Define potential difference.
The work done (energy transferred) per unit charge between two points.
Why does the resistance of a filament lamp increase as the current increases?
The filament gets hotter, so its ions vibrate more and impede the flow of electrons more.
Jobs that use this
Each link opens the job profile on the National Careers Service (England). In the rest of the UK: My World of Work (Scotland), Careers Wales, nidirect careers (Northern Ireland).
Ces fiches sont en anglais car elles suivent les programmes d'examen britanniques.
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