Resistance and I–V graphs Cambridge International AS & A Level Physics revision
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In plain words
Resistance tells you how much voltage it takes to push a given current through something. For a plain metal wire kept cool, that number stays the same whatever you do. For a lamp, a diode or a thermistor it changes, and a graph of current against voltage shows how.
4 things to know
- Resistance R = V ÷ I. Ohm's law: for a conductor at constant temperature, the current through it is proportional to the p.d. across it.
- I–V graphs: a metal at constant temperature gives a straight line through the origin. A filament lamp gives a curve that flattens, because its resistance rises as it heats up. A semiconductor diode conducts in one direction only, and only once the p.d. reaches about 0.6 V.
- Why temperature matters: in a hotter metal the ions vibrate more, so the electrons collide with them more often and the resistance rises. In a thermistor (the usual, negative temperature coefficient kind), heating frees many more charge carriers, so its resistance falls.
- In a light-dependent resistor (LDR), light frees more charge carriers, so its resistance falls as the light gets brighter.
Worked example
The I–V graph of a filament lamp passes through (2.0 V, 0.40 A) and (6.0 V, 0.60 A). Find its resistance at each point.
- At 2.0 V: R = 2.0 ÷ 0.40 = 5.0 Ω.
- At 6.0 V: R = 6.0 ÷ 0.60 = 10 Ω.
- The resistance has doubled, because the filament is much hotter.
Tips and tricks
- Resistance is V ÷ I at a point on the graph. It is not the gradient, unless the line is straight and passes through the origin.
- Check which quantity is on which axis before you describe a graph: some are drawn as I against V and some as V against I.
It lands in your notebook with its questions as flashcards.
Resistance and I–V graphs: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What does the I–V graph of a metal wire at constant temperature look like?
Current is proportional to p.d.
What happens to the resistance of a thermistor when its temperature rises?
Heating frees more charge carriers.
What happens to the resistance of an LDR when the light on it gets brighter?
Light frees more charge carriers.
A component has a p.d. of 12 V across it and carries a current of 0.25 A. What is its resistance?
R = V ÷ I.
Why does the resistance of a metal wire rise when it gets hotter?
The number of free electrons stays about the same.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Resistance and I–V graphs
Cambridge International AS & A Level Physics 9702 · 7 marks · papermunch.org
Name ______________________________ Date ______________
Explain why the resistance of a filament lamp increases as the current through it increases.[2]
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The filament gets hotter. Its ions vibrate more, so the electrons collide with them more often.
Describe the I–V graph of a semiconductor diode.[2]
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In the forward direction almost no current flows until the p.d. reaches about 0.6 V, and then the current rises steeply. In the reverse direction the current is almost zero.
A thermistor has a p.d. of 6.0 V across it. As it is warmed, the current through it rises from 2.0 mA to 12 mA. Find its resistance before and after.[3]
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3000 Ω before and 500 Ω after.
Answers: Resistance and I–V graphs
- 1. The filament gets hotter. Its ions vibrate more, so the electrons collide with them more often.
- 2. In the forward direction almost no current flows until the p.d. reaches about 0.6 V, and then the current rises steeply. In the reverse direction the current is almost zero.
- 3. 3000 Ω before and 500 Ω after.