Resistance, Ohm's law, I-V characteristics of a metal, filament lamp and diode, resistivity, and the effect of temperature.

What this dot point is asking

WJEC wants you to define resistance, state Ohm's law, sketch and explain the I-V characteristics of a metal, a filament lamp and a diode, and use resistivity to relate resistance to a conductor's dimensions. The distinction between ohmic and non-ohmic behaviour, and the resistivity practical, generate a steady supply of exam marks across both calculation and explanation questions.

The answer

Resistance and Ohm's law

Ohm's law states that the current through an ohmic conductor is proportional to the potential difference across it, provided the temperature stays constant. A component obeys Ohm's law only if its resistance is constant, which is why the law is really a special case rather than a universal rule.

I-V characteristics

Resistivity

Resistivity $\rho$ is a property of the material (in ohm metres). Resistance increases with length and decreases with cross-sectional area. Measuring the resistivity of a wire is a specified practical: plot $R$ against $\dfrac{L}{A}$ and the gradient is $\rho$.

Effect of temperature

In a metal, raising the temperature makes the lattice ions vibrate more, scattering electrons and increasing resistance. In a semiconductor (such as a thermistor), warming releases more charge carriers, so resistance falls.

Examples in context

Example 1. Why power lines use thick aluminium

Overhead transmission lines must keep resistance low to limit the $I^2 R$ heating losses over hundreds of kilometres. Since $R = \rho L / A$, the length is fixed but engineers make the cross-section $A$ large; aluminium is chosen because, although its resistivity is slightly higher than copper, it is far lighter and cheaper for the same low resistance.

Example 2. A diode protecting a circuit

Because a diode conducts only in forward bias above about $0.6\,\text{V}$ and blocks reverse current, it is placed in series to protect electronics from a battery inserted the wrong way round. Its strongly non-ohmic I-V characteristic is exactly the property that makes it useful as a one-way valve for current.

Example 3. A thermistor temperature probe

A thermistor is a semiconductor whose resistance falls sharply as it warms, the opposite of a metal. Placed in a potential divider, its changing resistance produces a voltage that varies with temperature, which a microcontroller reads to display a value. This negative temperature coefficient, explained by the rising carrier density in a semiconductor, is what makes thermistors the sensor of choice in everything from kettles to engine management systems.

Try this

Q1. A wire of length $2.0\,\text{m}$ and cross-sectional area $5.0\times10^{-7}\,\text{m}^2$ has resistance $1.8\,\Omega$. Find its resistivity. [2 marks]

• Cue. $\rho = \frac{RA}{L} = \frac{1.8\times5.0\times10^{-7}}{2.0} = 4.5\times10^{-7}\,\Omega\,\text{m}$.

Q2. Explain why the resistance of a metallic conductor rises with temperature. [2 marks]

• Cue. Lattice ions vibrate more, scattering the electrons more often, so resistance increases.