8.3 - V = IR Equation & I-V Graphs

Formula linking p.d., current and resistance

Where:

• $V$ = Potential difference, in volts (V)
• $I$ = Current, in amperes (A)
• $R$ = Resistance, in ohms (Ω)

The greater the resistance of a component, the smaller the current that flows through it for a given potential difference across it.

Finding the resistance

The equation can be rearranged to find the resistance of a component from measured values of potential difference and current:

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

Worked example - Current through a resistor

A 5.0 Ω resistor in a circuit has a potential difference of 9.0 V across it. Calculate the current through the resistor.

Ohmic conductors and the V-I characteristic

• A V-I characteristic is a graph showing how the voltage (also called the potential difference) across a component changes as the current through it is increased - voltage on the y-axis, current on the x-axis.
• The resistance of an ohmic conductor, such as a fixed resistor or a metal wire, does not change with the current through it - as long as its temperature stays constant.
• For an ohmic conductor at constant temperature, the current is directly proportional to the voltage across it. This is commonly called Ohm's law.

Shape of the graph

• A component whose resistance stays constant gives a straight line through the origin.
• The steeper the line, the higher the resistance.

Finding the resistance from the graph

• Read the voltage and current at a point and use $R=\frac{V}{I}$.
• For a straight line through the origin, the resistance is the gradient of the line.

V-I characteristic of a filament lamp

• Some components do not have a constant resistance, so their V-I characteristic (voltage on the y-axis, current on the x-axis) is a curve rather than a straight line. The filament lamp is one of these.
• As the current through a filament lamp increases, the free electrons collide more often with the atoms of the filament and transfer energy to them, so the filament heats up.
• As its temperature rises, the resistance increases.
• The resistance at any point is the ratio of the voltage to the current ($R=\frac{V}{I}$), and this ratio gets larger as the current increases.
• Each extra amp of current needs a bigger increase in voltage, so the characteristic gets steeper as the current increases - giving a curve.
• The drawing shows the same curve with the axes the other way round (current up the side), so on it the curve flattens off instead.