Ohm's Law and Resistance
In one line
The current through a wire is directly proportional to the voltage across it, as long as its temperature stays the same.
The formula
V = I × R
| Symbol | Means | SI unit |
|---|---|---|
| V | Potential difference (voltage) | volt (V) |
| I | Current | ampere (A) |
| R | Resistance | ohm (Ω) |
Rearrange it as needed: I = V ÷ R and R = V ÷ I. A wire has a resistance of 1 Ω when a 1 V potential difference drives a current of 1 A through it.
Key points
- Resistance is how much a conductor opposes the flow of current.
- A V–I graph for a wire is a straight line through the origin. Its slope gives the resistance.
- Resistance increases with length: double the length, double the resistance.
- Resistance decreases as the wire gets thicker: it is inversely proportional to the cross-section area.
- It depends on the material. Copper and aluminium have low resistance; nichrome (used in heaters) has high resistance.
- For most metals, resistance rises with temperature.
- An ammeter is connected in series; a voltmeter is connected in parallel.
R = ρ × l ÷ A
ρ (rho) is resistivity, measured in ohm metre (Ω m). l is length in metres, A is cross-section area in m².
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Series and parallel
| Series | Parallel | |
|---|---|---|
| Total resistance | R = R₁ + R₂ + R₃ | 1/R = 1/R₁ + 1/R₂ + 1/R₃ |
| Current | Same through each resistor | Splits between branches |
| Voltage | Splits between resistors | Same across each resistor |
| Result | Total is bigger than the largest | Total is smaller than the smallest |
| Used in | Old fairy lights | House wiring (each appliance gets full voltage) |
Solved examples
1. Find the currentA 4 Ω resistor is connected to a 12 V battery. I = V ÷ R = 12 ÷ 4 = 3 A.
2. Series2 Ω and 3 Ω in series: R = 2 + 3 = 5 Ω.
3. Parallel6 Ω and 3 Ω in parallel: 1/R = 1/6 + 1/3 = 1/6 + 2/6 = 3/6, so R = 2 Ω.
Common mistakes
- Forgetting to flip at the end in parallel. 1/R = 1/2 means R = 2 Ω, not 0.5 Ω.
- Mixing units. Change mA to A (÷ 1000) and kΩ to Ω (× 1000) before using V = IR.
- Saying Ohm's law always holds. It holds only at constant temperature and for ohmic conductors like metal wires.
Quick check
Revise in 30 seconds
| Ohm's law | V = IR (constant temperature) |
|---|---|
| Depends on | Length ↑ R ↑ · Area ↑ R ↓ · Material · Temperature |
| Resistivity | R = ρl ÷ A; ρ in Ω m |
| Series | R = R₁ + R₂ + … |
| Parallel | 1/R = 1/R₁ + 1/R₂ + … |
| Meters | Ammeter in series · Voltmeter in parallel |