I-V Characteristics

This lesson covers the current-voltage (I-V) characteristics of key components, as required by the Edexcel GCSE Combined Science specification (1SC0). You must be able to describe, sketch and interpret I-V graphs for a resistor, filament lamp and diode.

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What Is an I-V Characteristic?

An I-V characteristic is a graph that shows how the current (I) through a component changes as the potential difference (V) across it changes.

• The x-axis shows potential difference (V).
• The y-axis shows current (I) in amps (A).
• The graph often extends into negative values of V and I to show what happens when the voltage is reversed.

How to Obtain I-V Data

1. Set up the component in a circuit with a variable resistor (or variable power supply), an ammeter in series and a voltmeter in parallel.
2. Start with the lowest voltage and gradually increase it.
3. Record the voltage (V) and current (I) at each setting.
4. Reverse the connections to the battery and repeat for negative voltages.
5. Plot V on the x-axis and I on the y-axis.

flowchart LR
    A["Variable Power Supply"] --> B["Ammeter (A)"]
    B --> C["Component"]
    C --> A
    C -. "Voltmeter (V)" .-> B

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1. Ohmic Conductor (Fixed Resistor)

Shape of the Graph

The I-V graph for a fixed resistor at constant temperature is a straight line through the origin.

Description

Feature	Detail
Shape	Straight line through the origin
Gradient	Constant — the resistance does not change
Symmetry	Symmetrical through the origin — same behaviour when voltage is reversed
Resistance	Constant at all values of V and I

What It Means

• Current is directly proportional to voltage.
• The component obeys Ohm's law.
• The resistance can be found from the gradient: $R = \frac{V}{I}$R=IV​ at any point, or from the inverse of the gradient if I is on the y-axis.

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2. Filament Lamp

Shape of the Graph

The I-V graph for a filament lamp is a curved line that passes through the origin. The curve becomes shallower (flatter) at higher voltages.

Description

Feature	Detail
Shape	S-shaped curve through the origin
At low voltage	Nearly straight — behaves almost ohmically
At high voltage	Curve flattens — current increases more slowly
Symmetry	Symmetrical through the origin
Resistance	Increases as voltage and current increase

Why the Resistance Increases

• As current increases, the filament gets hotter.
• Hotter metal ions vibrate more vigorously.
• Electrons collide with the ions more often.
• These extra collisions mean greater opposition to current flow, so resistance increases.

Exam Tip: When describing the filament lamp graph, always link the shape to temperature. Say: "As the current increases, the filament heats up, causing the resistance to increase, so the graph curves."

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3. Diode

Shape of the Graph

The I-V graph for a diode shows current flowing in one direction only (forward bias). In the reverse direction, no current flows.

Description

Feature	Detail
Forward bias (positive V)	Current flows once V exceeds about 0.6–0.7 V (for a silicon diode), then increases steeply
Reverse bias (negative V)	No current flows (or negligible leakage current)
Symmetry	Not symmetrical — the diode has very different behaviour in each direction
Resistance	Very high in reverse bias; very low in forward bias above the threshold

Key Point

A diode acts as a one-way valve for current. It only allows conventional current to flow in the direction of the arrow in the circuit symbol (from anode to cathode).

LED (Light-Emitting Diode)

An LED behaves like a diode but also emits light when forward biased. The threshold voltage varies depending on the colour of the LED.

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Comparing the Three Graphs

Component	Graph Shape	Obeys Ohm's Law?	Resistance
Fixed resistor	Straight line through origin	Yes	Constant
Filament lamp	S-shaped curve through origin	No	Increases with current
Diode	Current in one direction only	No	Very high in reverse; very low in forward

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Calculating Resistance from an I-V Graph

At any point on an I-V graph, resistance can be calculated using:

$R = \frac{V}{I}$R=IV​

Worked Example

At a particular point on a filament lamp I-V graph, V = 6 V and I = 0.4 A. What is the resistance?

$R = \frac{6}{0.4} = 15 \; \Omega$R=0.46​=15Ω

At a higher voltage, V = 10 V and I = 0.5 A. What is the resistance now?

$R = \frac{10}{0.5} = 20 \; \Omega$R=0.510​=20Ω

The resistance has increased from 15 $\Omega$Ω to 20 $\Omega$Ω because the filament is hotter.

Exam Tip: To show that resistance changes on a curved I-V graph, calculate $R = V/I$R=V/I at two different points and compare the values. This is a common 3–4 mark question.

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Thermistor and LDR (Brief Overview)

Although their I-V graphs are not required in detail, you must know how their resistance changes:

Component	As temperature increases...	As light intensity increases...
Thermistor	Resistance decreases	—
LDR	—	Resistance decreases

These components are used in sensing circuits — for example, a thermistor in a thermostat or an LDR in an automatic streetlight.

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Core Practical: Investigating I-V Characteristics

The Edexcel specification includes a core practical on this topic:

1. Set up a circuit with the component, a variable resistor, ammeter and voltmeter.
2. Record at least six pairs of V and I values.
3. Reverse the battery connections and record negative V and I values.
4. Plot the I-V graph.
5. Identify whether the component obeys Ohm's law.

Control Variables

• Use the same component throughout.
• Record readings quickly to minimise heating effects (especially for the filament lamp).

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Summary

• An I-V characteristic shows how current through a component varies with voltage.
• A fixed resistor gives a straight line through the origin — constant resistance, obeys Ohm's law.
• A filament lamp gives an S-shaped curve — resistance increases as the filament heats up.
• A diode allows current in one direction only — very high resistance in reverse bias.
• Resistance at any point on an I-V graph is calculated using $R = \frac{V}{I}$R=IV​.
• A thermistor's resistance decreases with temperature; an LDR's resistance decreases with light intensity.

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Extended Worked Examples

Worked Example 2 — Filament Lamp Data

A filament lamp gives the data below. Show that the resistance increases with voltage.