What resistance is
- Resistance is the opposition a component offers to the flow of electric current through it
- The greater the resistance, the harder it is for charge to flow, and so the smaller the current for a given voltage
- Resistance is measured in ohms, symbol Ω (the Greek capital omega)
- A component has a resistance of 1 Ω when a voltage of 1 V across it drives a current of exactly 1 A through it (so 1 Ω = 1 V/A)
What sets the resistance of a component
- Material: good conductors like copper and silver have very low resistance; insulators like rubber and dry wood have enormous resistance
- Length: a long wire has more resistance than a short one of the same material and thickness, because every extra metre adds to the obstruction
- Cross-sectional area: a thick wire has less resistance than a thin one, because there is more room for charge to flow
- Temperature: in most metals, resistance rises as temperature rises; the metal ions vibrate harder and collide with the drifting electrons more often
- Even the connecting wires themselves have a small resistance, but in exam circuits they are taken to be zero unless the question states otherwise
Ohm's law: V = I × R
- The defining equation linking voltage, current and resistance is:
V = I × R
- where:
- V = voltage across the component (V)
- I = current through the component (A)
- R = resistance of the component (Ω)
- Rearrangements:
- I = V / R (current is voltage divided by resistance)
- R = V / I (resistance is voltage divided by current, which is the experimental way to measure R)
- A component is said to be ohmic if its resistance is constant across the working range (V is then directly proportional to I). Many resistors and lengths of metal wire at a steady temperature behave this way; filament lamps and diodes do not, and so are non-ohmic (covered fully in topic 06)
Example — a current of 0.40 A flows through a 25 Ω resistor. Calculate the voltage across the resistor.
- V = I × R = 0.40 × 25 = 10 V
Example — a 12 V battery drives a current of 0.30 A through a heater. Calculate the heater's resistance.
- Rearrange Ohm's law: R = V / I = 12 / 0.30 = 40 Ω
Idealisations on circuit diagrams
- In IGCSE exam questions, unless stated otherwise:
- the wires have zero resistance
- the internal resistance of the cell or battery is zero
- an ammeter has zero resistance and so does not alter the current it is reading
- a voltmeter has infinite resistance and so draws no current away from the component it is reading
- These idealisations make the algebra clean; in real life, every one of them is a small approximation rather than an exact truth