The big idea: Resistance measures how hard it is to push current (the flow of charge) through a component.
A bigger resistance means a bigger voltage (the push) is needed for the same current.
Resistance is voltage ÷ current, and its unit is the ohm (Ω).
[Diagram: phys-circuit] - Available in full study mode
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.
Ohm's law 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)
[Diagram: phys-formula-triangle] - Available in full study mode
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.
Worked example — resistance from an I–V graph
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.
Solution
- Start with the given formula (Ohm's law):
- Rearrange to make R the subject:
- Put in the numbers from the point (V = 6.0, I = 1.5):
- Work it out — keep the unit:
Final answer
R = 4.0 Ω. The line is straight, so every point gives the same 4.0 Ω.
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How this is tested: Resistance and Ohm's law are the backbone of the circuit questions.
- Paper 1A / 2: read a resistance off an I–V graph (R = V ÷ I at a point), or 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.
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).
IB-style question — (a) ohmic or non-ohmic?
Component P has a straight I–V line through the origin; component Q has a curved I–V graph that bends towards the voltage axis. State, with a reason, which component is ohmic.
Solution
- Ohmic means R is constant, which shows up as a straight I–V line through the origin.
- P's line is straight → R = V ÷ I is the same everywhere → P is ohmic.
- Q's graph is curved, so R = V ÷ I changes with the current → Q is non-ohmic.
Final answer
P is the ohmic component — its I–V graph is a straight line through the origin, so its resistance is constant.
IB-style question — (b) how Q's resistance changes
Component Q is a filament lamp. Outline how the resistance of Q changes as the current through it increases.
Solution
- A larger current heats the filament, so its temperature rises.
- A hotter metal wire resists current more, so its resistance increases.
Final answer
As the current increases the filament gets hotter, so the resistance of Q increases.