3.4 - 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.

I-V characteristics of filament lamps and diodes

• Some components do not have a constant resistance, so their I-V characteristic is a curve rather than a straight line.
• Components with a curved I-V characteristic are called non-linear components.

The filament lamp

• As the current through a filament lamp increases, the moving charges transfer energy to the thermal energy store of the filament, so the filament heats up.
• As the temperature rises, the metal ions vibrate more, and electrons collide with them more often, so the resistance increases.
• Because the resistance rises, less current flows for each extra volt, so the characteristic gets shallower as the potential difference increases - giving a curve.

The diode

• A diode lets current flow through it in one direction only.
• It has a very high resistance in the reverse direction, so almost no current flows that way.
• The I-V characteristic is flat (zero current) for a reverse potential difference, then curves upwards once the potential difference is in the forward direction.
• A light-emitting diode (LED) is a type of diode that emits light when current flows through it in the forward direction.