3.3.1 Voltage-Current (V-I) Graphs

3.3.1 Voltage-Current (V-I) Graphs: Interpret voltage-current graphs for a fixed resistor and a filament lamp, and use the gradient to find resistance.

The relationship between voltage and current shows how a component behaves.

Method

Vary the potential difference across a component and record the current at each setting.

Plotting

Plot voltage on the vertical axis and current on the horizontal axis to make a V-I graph.

Resistance

Resistance is the ratio V ÷ I, which is the gradient of a V against I graph.

Unit

Resistance is measured in ohms (Ω), where 1 Ω = 1 V/A.

Different components give different characteristic curves.

Shapes of Graphs

Fixed resistor

A straight line through the origin shows that current is directly proportional to voltage and resistance is constant.

Filament lamp

A curve whose gradient increases shows that resistance rises as the filament gets hotter.

Ohmic conductor

Any component whose V-I graph is a straight line through the origin obeys Ohm's law.

Diode

A diode conducts in one direction and has a very high resistance in the opposite direction.

Component	Graph shape	Resistance
Fixed resistor	Straight line through origin	Constant
Filament lamp	Curve getting steeper	Increases with temperature

Read values carefully from the axes and apply R = V ÷ I.

Choose a point on the line and read the voltage from the vertical axis.

Read the matching current from the horizontal axis, checking whether it is in amps or milliamps.

Divide the voltage by the current to find the resistance at that point.

For a straight line the answer is the same at every point, so the resistor is ohmic.

For a curve the value changes, so quote the resistance at the voltage asked for.

Question: A filament lamp passes 0.20 A at 6.0 V and 0.30 A at 12 V. Calculate its resistance at each point and comment.

At 6.0 V: R = V ÷ I = 6.0 ÷ 0.20 = 30 Ω.
At 12 V: R = 12 ÷ 0.30 = 40 Ω.
The resistance has increased as the filament got hotter.

Answer: R = 30 Ω at 6.0 V and 40 Ω at 12 V; resistance rises with temperature.

3.3.1 – Key Points for the Exam

V-I graph: A graph of potential difference against current for a component.
Ohmic conductor: A conductor with constant resistance at constant temperature.
Gradient: The slope of the line, equal to resistance on a V against I graph.
Filament lamp: A lamp whose resistance rises as the filament heats up.

Common Mistakes

Calling a curved lamp graph a proportional relationship.
Reading the gradient as I ÷ V instead of V ÷ I when voltage is on the vertical axis.
Forgetting to convert milliamperes to amperes before finding resistance.
Saying that resistance of the lamp falls as it brightens; it increases.