# 2.1.6 I–V Graphs

### Ohm's Law

• Ohm’s Law states that:

The current through a conductor is directly proportional to the potential difference across it

• Electrical conductors that obey Ohm’s Law are referred to as ohmic conductors
• Examples of ohmic conductors are:
• Fixed resistors
• Wires
• Heating elements
• Ohm’s Law is represented by the equation V = IR
• If V and I are directly proportional, this means that the resistance R remains constant
• Ohm’s Law is relevant only at constant temperatures
• An ohmic conductor will have a current-voltage (I–V) graph that is a straight line through the origin

An I-V graph for an ohmic conductor is a straight line graph through the origin

• Reversing the potential difference (and direction of the current) makes no difference to the shape of the line, the potential difference and current values will just be negative
• If the axis labels are swapped around (the current on the x-axis and p.d on the y-axis) the graph will still be a straight line through the origin

### Filament Lamps

• A filament lamp is an example of a non-ohmic conductor
• This means that the current and potential difference are not directly proportional
• This is because the resistance of the filament lamp increases as the temperature of the filament increases
• The I–V graph for a filament lamp shows the current increasing at a proportionally slower rate than the potential difference

I-V graph for a filament lamp

• This is because:
• As the current increases, the temperature of the filament in the lamp increases
• The higher temperature causes the atoms in the metal lattice of the filament to vibrate more
• This causes an increase in resistance as it becomes more difficult for free electrons (the current) to pass through
• Resistance opposes the current, causing the current to increase at a slower rate
• Where the graph is a straight line, the resistance is constant
• The resistance increases as the graph curves
• Reversing the potential difference reverses the current and makes no difference to the shape of the curve

#### Resistance & Temperature

• All solids are made up of vibrating atoms
• The higher the temperature, the faster these atoms vibrate
• Electric current is the flow of free electrons in a material
• The electrons collide with the vibrating atoms which impedes their flow, hence the current decreases
• So, if the current decreases, then the resistance will increase (from V = IR)
• Therefore, an increase in temperature causes an increase in resistance

### Diodes

• A diode is a non-ohmic conductor that allows current to flow in one direction only
• This is called forward bias
• In the reverse direction, the diode has very high resistance, and therefore no current flows
• This is called reverse bias

• The I–V graph for a diode is slightly different:
• When the current is in the direction of the arrowhead symbol, this is forward bias
• This is shown by the sharp increase in potential difference and current on the right side of the graph
• When the diode is switched around, this is reverse bias
• This is shown by a zero reading of current or potential difference on the left side of the graph

I-V graph for a semiconductor diode

• An LED is a specific type of diode that emits light and works the same way as a normal diode

### Linear & Non-Linear Graphs

• Circuit elements can be linear or non-linear
• In maths, linear means the graph is a straight line
• To know whether a circuit element is linear or non-linear, check whether its I-V graphs is a straight line or not
• Linear components have an I-V graph that is a straight line through the origin
• Non-linear components have an I-V graph that is not a straight line
• Linear components are said to obey Ohm’s Law and have a constant resistance, whilst non-linear do not
• Some components may be linear at low currents, then become non-linear as the current increases (and therefore a change in temperature)
• For example, a fixed resistor at room temperature is linear, but when it becomes very hot it will become non-linear

Linear and non-linear I-V graphs

• Linear elements include:
• Fixed resistors
• Wires
• Heating elements
• Non-linear elements include:
• Filament lamps
• Diodes & LEDs
• LDRs
• Thermistors

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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