I–V Graphs

Section 1 of 7Reading an I–V graph

What is plotted

• What is plotted An I–V graph shows how the current I through a component changes as the potential difference V across it is varied.
• Conventionally current is on the y-axis and potential difference on the x-axis.

Link to resistance

• Link to resistance Resistance is found from R = V ÷ I, so it can be worked out from any single point on the graph.
• The resistance is not simply the gradient unless the graph is a straight line through the origin.

Reversing the cell

• Reversing the cell Swapping the connections to the power supply reverses the current, so the graph continues into the negative quadrants.
• For an ohmic conductor and a filament lamp the negative part is a mirror image of the positive part.

Section 2 of 7Ohmic conductors

Straight line through the origin

Ohm's law

• Ohm's law At constant temperature the current through an ohmic conductor is directly proportional to the potential difference across it.

Constant resistance

• Constant resistance Doubling V doubles I,
  • so the ratio V ÷ I never changes: V = I × R.
    What the symbols mean: V = potential difference (V) · I = current (A) · R = resistance (Ω)

Examples

• Examples Fixed resistors and metal wires kept at a constant temperature.

Steepness

• Steepness A steeper line means a larger current for the same p.d., so a smaller resistance.

Section 3 of 7Why a filament lamp curves

1Current flows

• Current flows Electrons collide with the metal ions of the filament, transferring energy to them.

2Filament heats up

• Filament heats up The ions vibrate with larger amplitude as the temperature rises.

3More collisions

• More collisions Electrons are obstructed more often, so it is harder for charge to flow.

4Resistance increases

• Resistance increases Current rises by less and less for each equal step in p.d., so the graph flattens into a curve.

Section 4 of 7Comparing components

Component	Shape of I–V graph	Resistance behaviour
Fixed resistor	Straight line through the origin	Constant
Filament lamp	S-shaped curve, steeper near the origin	Increases as the filament gets hotter
Diode	Almost no current in reverse; current rises sharply once forward p.d. passes about 0.6 V	Very high in reverse, low in the forward direction
Thermistor (NTC)	Curve getting steeper as it warms	Decreases as temperature rises

Section 5 of 7Diode in detail

1

A diode only allows current to pass in one direction, the direction of the arrowhead in its symbol.

2

In the forward direction the current is negligible until the p.d. reaches a threshold of a few tenths of a volt.

3

Above the threshold the current increases rapidly, so the resistance drops.

4

In the reverse direction the resistance is so high that the current is effectively zero.

Section 6 of 7Key terms

Term	Meaning
Ohmic conductor	A conductor whose current is directly proportional to p.d. at constant temperature.
Non-ohmic conductor	A component whose resistance changes as the current or conditions change, giving a curved I–V graph.
Potential difference	The energy transferred per unit charge between two points, measured in volts.
Resistance	A measure of how much a component opposes current, found using R = V ÷ I and measured in ohms (Ω).
Diode	A component that lets current flow in one direction only.

Section 7 of 7Exam technique

1

Saying the resistance of a lamp is the gradient of its curve — use R = V ÷ I at a chosen point instead.

2

Claiming the filament lamp's resistance increases because the current is bigger without mentioning the rise in temperature.

3

Thinking a steeper I–V line means a larger resistance — it means a smaller one, because more current flows per volt.

4

Forgetting that a graph with the axes swapped (V against I) has its steep and shallow meanings reversed.