I–V Graphs (AQA GCSE Physics: Combined Science)

• 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

• 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

• 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

• 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