1.2 - 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 I-V characteristic

• An I-V characteristic (or current-voltage characteristic) is a graph showing how the current through a component changes as the potential difference across it is increased.
• 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 potential difference across it.

Shape of the graph

• A component whose resistance stays constant gives a straight line through the origin.
• Components with a straight-line characteristic are called linear components.
• The steeper the line, the lower the resistance.

Finding the resistance from the graph

• Read the potential difference and current at a point and use $R=\frac{V}{I}$.
• For a linear component whose line passes through the origin, the resistance is the inverse of the gradient.