Ohm's law and the V-I graph
At constant temperature, current through a conductor is directly proportional to the potential difference across it (V = IR). Its V-I graph is a straight line through the origin.
The law
In 1827 the German physicist Georg Simon Ohm found a simple rule. If the temperature stays the same, the potential difference V across a metal wire is directly proportional to the current I through it. So V/I stays constant. This constant is the resistance R of the wire, and V = IR. Resistance is the property of a conductor that opposes the flow of charge. For the same potential difference, doubling R halves the current, because I = V/R. A rheostat is a variable resistance used to change the current in a circuit.
Activity: V-I graph for a resistor
You need a nichrome wire XY (or a resistor), an ammeter, a voltmeter, a plug key and four 1.5 V cells.
- 1Join one cell, the plug key, the ammeter and the wire XY in series. Connect the voltmeter across XY.
- 2Close the key. Note the current I from the ammeter and the potential difference V from the voltmeter.
- 3Repeat with two, three and then four cells in the circuit. Note I and V each time.
- 4Work out V/I for each pair of readings, and plot V against I on a graph.
- 5Observation: V/I is nearly the same every time, and the graph is a straight line through the origin. This verifies Ohm's law.
How to draw the circuit and the graph
- Circuit: draw a battery of cells in a row and mark its + and − ends.
- From the + end, draw a wire to a plug key and then an ammeter (A in a circle).
- Next draw a zigzag resistor labelled XY, and join it back to the − end.
- Draw the voltmeter (V in a circle) in parallel across XY only.
- Mark the + terminal of each meter towards the + end of the battery, and add an arrow for the direction of current.
- Graph: draw two axes. Label the x-axis Current I (A) and the y-axis Potential difference V (V).
- Plot the points and draw one straight line through them that passes through the origin O. Write slope = V/I = R beside it.
- Check the axes in every question. If V is on the x-axis and I is on the y-axis, the slope is I/V = 1/R, so the steeper line belongs to the smaller resistance.
Worked example: using V = IR
(a) An electric heater draws a current of 4 A from a 220 V supply. Find its resistance. (b) What current flows through a 20 Ω resistor when the potential difference across it is 12 V?
- (a) Given: V = 220 V, I = 4 A.
- Formula: R = V/I.
- R = 220 V ÷ 4 A = 55 Ω.
- (b) Given: R = 20 Ω, V = 12 V.
- Formula: I = V/R.
- I = 12 V ÷ 20 Ω = 0.6 A.
(a) 55 Ω; (b) 0.6 A
Worked example: reading data from an experiment
A student records these readings for a resistor. V: 1.0 V, 2.0 V, 3.0 V, 4.0 V. I: 0.2 A, 0.4 A, 0.6 A, 0.8 A. Does the resistor obey Ohm's law? Find its resistance, and the current at 2.5 V.
- V/I for each pair: 1.0 ÷ 0.2 = 5; 2.0 ÷ 0.4 = 5; 3.0 ÷ 0.6 = 5; 4.0 ÷ 0.8 = 5.
- V/I is constant, so the resistor obeys Ohm's law.
- R = V/I = 5 Ω.
- At V = 2.5 V: I = V/R = 2.5 V ÷ 5 Ω = 0.5 A.
Yes, it obeys Ohm's law; R = 5 Ω; current at 2.5 V = 0.5 A
Older ceiling fan regulators worked by changing the resistance in the circuit: more resistance, less current, slower fan. A rheostat in the school lab does the same job.
1 marks: “State Ohm's law.” At constant temperature, the current through a conductor is directly proportional to the potential difference across its ends: V = IR.
3 marks: “A bulb draws 0.5 A from a 220 V supply. Find its resistance. What current would it draw at 110 V, if its resistance stays the same?” R = V/I = 220 ÷ 0.5 = 440 Ω. At 110 V: I = 110 ÷ 440 = 0.25 A.
5 marks: “Describe an activity to verify Ohm's law. Draw the circuit diagram and the graph you expect.” Circuit with cells, key, ammeter and nichrome wire in series, voltmeter across the wire; readings with 1 to 4 cells; V/I constant; straight-line V-I graph through the origin.
V = IR, the VIR triangle: cover V to get I × R, cover I to get V/R, cover R to get V/I.