I-V Characteristics

Overview

An I-V characteristic describes how the current $I$ through a component varies with the potential difference $V$ across it. The shape of the graph reveals whether a component is ohmic or non-ohmic, and how its resistance changes under different operating conditions.

This page deepens ideas introduced in Current Electricity Fundamentals.

Related topics:

• DC Circuits
• Electrical Power and Ratings
• Current Electricity Common Exam Traps

Definition

An I-V characteristic is a graph showing the relationship between:

• current $I$ through a component
• potential difference $V$ across the component

Unless otherwise stated, the usual graph is current $I$ against potential difference $V$:

• horizontal axis: $V$
• vertical axis: $I$

Always check axes before interpreting gradient.

Why It Matters

They help you determine:

• whether a component obeys Ohm’s law
• whether resistance is constant
• how resistance changes with temperature or bias
• suitable operating region of a device
• current for a given voltage

Key Representations

Ohmic vs Non-Ohmic Behaviour

Ohmic Component

A component is ohmic if:

$$V\propto I$$

at constant temperature.

So:

• straight-line graph through origin
• constant resistance

Non-Ohmic Component

A component is non-ohmic if:

• graph is curved, asymmetric, or changes slope
• resistance varies with voltage, current, temperature, or light

Examples:

• filament lamp
• diode
• thermistor
• LDR

Interpreting Resistance from Graphs

Resistance is:

$$R=\frac{V}{I}$$

At a chosen operating point:

• large $V/I$ ratio → large resistance
• small $V/I$ ratio → small resistance

Gradient Meaning

If Graph is $I$ Against $V$

Gradient:

$$\frac{\Delta I}{\Delta V}$$

For ohmic conductor:

$$\frac{I}{V}=\frac{1}{R}$$

So:

• steeper line → lower resistance
• shallower line → higher resistance

If Graph is $V$ Against $I$

Gradient gives:

$$R$$

Always check axis labels.

Metallic Conductor at Constant Temperature

Behaviour

A metallic resistor maintained at constant temperature obeys Ohm’s law.

$$V=IR$$

Graph Shape

• straight line
• passes through origin

Filament Lamp

A filament lamp is non-ohmic.

As current increases:

• filament temperature rises
• lattice ions vibrate more strongly
• electron-ion collision rate increases
• resistance increases

On an $I$ against $V$ graph, the curve becomes less steep at larger $V$ because:

$$\text{gradient}=\frac{1}{R}$$

and $R$ has increased.

Semiconductor Diode

A diode conducts easily in forward bias and conducts very little in reverse bias.

Forward bias:

• very small current below turn-on p.d.
• current rises rapidly after threshold
• resistance becomes low

Reverse bias:

• current is approximately zero for normal reverse p.d. values
• resistance is very high

A diode is strongly non-ohmic.

Thermistor

An NTC thermistor has resistance that decreases as temperature increases.

For an NTC thermistor:

$$T\uparrow \Rightarrow R\downarrow$$

Reason:

• heating increases the number density of mobile charge carriers
• this effect outweighs increased collision rate

Light-Dependent Resistor

For an LDR:

$$\text{light intensity}\uparrow \Rightarrow R\downarrow$$

More light produces more mobile charge carriers.

Experimental Setup

To obtain an I-V characteristic, use:

• component under test
• ammeter in series
• voltmeter in parallel
• variable resistor or potential divider
• d.c. supply
• switch

Vary the potential difference and record pairs of $V$ and $I$.

Precautions:

• keep temperature constant for an ohmic conductor
• use small currents if heating must be minimised
• reverse connections where negative p.d. values are needed
• take enough readings to show graph shape

Worked Example

A resistor has p.d. $4.0\text{ V}$ and current $0.50\text{ A}$.

$$R=\frac{V}{I}=\frac{4.0}{0.50}=8.0\Omega$$

If this point lies on a straight line through the origin with similar nearby points, the component is consistent with ohmic behaviour at that temperature.

Common Exam Traps

Gradient Confusion

On an $I$ against $V$ graph, gradient is $1/R$, not $R$.

Assuming All Straight Lines Mean Ohm’s Law

The line must pass through the origin and physical conditions such as temperature must remain constant.

Saying Current Is Blocked Completely in Reverse Bias

At this level, reverse current is often treated as negligible, but real diodes may have tiny leakage current.

Forgetting Temperature Effects

For a filament lamp, resistance changes mainly because the filament heats up.

Confusing Thermistor and Metal Behaviour

Metal resistance usually increases with temperature. NTC thermistor resistance decreases with temperature.

For a compact revision warning sheet, see:

Current Electricity Common Exam Traps

Summary Comparison Table

Component	I-V Behaviour	Resistance Trend
Ohmic resistor	Straight line through origin	Constant at constant temperature
Filament lamp	Curve flattens on $I$-$V$ graph	Increases as temperature rises
Diode	Conducts mainly in forward bias	Very direction-dependent
NTC thermistor	Depends on self-heating / temperature	Decreases as temperature rises
LDR	Depends on illumination	Decreases as light intensity rises

Links

• Related: Current Electricity Fundamentals
• Related: Resistivity and Materials
• Related: DC Circuits
• Related: Current Electricity Common Exam Traps