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

Ohm's Law

• Ohm's law states that:

The current through an ohmic conductor is directly proportional to the potential difference across it, provided the temperature stays constant

• Electrical conductors that obey Ohm's Law are referred to as ohmic conductors

• Examples of ohmic conductors are:

  • Fixed resistors

  • Wires

• 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

• 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

• 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 (which carry 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

• On an I–V graph with current on the y-axis, a lower gradient means a higher resistance

• Reversing the potential difference reverses the current

  • The curve for negative values is the same shape turned through the origin (a smooth curve that gets less steep as it moves away from the origin, in the opposite direction)

• To find the resistance at a point, read the current and potential difference at that point and use $R=\frac{V}{I}$

• To compare two components, the one with the lower current for the same potential difference has the higher resistance

  • For example, a potential difference of 1.0 V and a current of 0.08 A gives $R=\frac{1.0}{0.08}=12.5\mathrm{\Omega }$

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 more often, which impedes their flow

• So, for the same potential difference, the current is smaller, and the resistance is larger (from $R=\frac{V}{I}$)

• 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 the current staying at zero (the graph lies along the potential difference axis) for all negative potential differences

• 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 graph 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 elements include:

  • Fixed resistors

  • Wires

• Non-linear elements include:

  • Filament lamps

  • Diodes & LEDs

  • LDRs

  • Thermistors