Revise Resistance and resistivity for Cambridge 9702 (9.3)

Resistance is a measure of how much a component opposes the flow of electric current. Imagine trying to run through a busy corridor – the more people (resistance), the harder it is to move quickly (current). A higher resistance means less current will flow for a given potential difference.

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

On a microscopic level, resistance in a metal conductor arises from collisions between the free-moving charge carriers (electrons) and the fixed positive ions that make up the crystal lattice. When a potential difference is applied, electrons are accelerated by the electric field, but these collisions hinder their overall progress, causing them to move with an average 'drift velocity'. The energy transferred during these collisions is dissipated as heat.

Ohm's Law describes a specific relationship where the current through a conductor is directly proportional to the potential difference across it, provided its temperature remains constant. Components that follow this rule are called ohmic conductors.

Not all components obey Ohm's Law. Non-ohmic conductors have resistance values that change depending on factors like temperature or current. Their I-V graphs are not linear, showing how their resistance varies.

A common example of a non-ohmic component is a filament lamp. As more current flows through the filament, it heats up significantly. This increase in temperature causes the metal atoms in the filament to vibrate more vigorously, making it harder for electrons to pass through.

Semiconductor diodes are another key non-ohmic component. They allow current to flow easily in one direction (forward bias) once a small threshold voltage is overcome, but offer very high resistance to current flow in the opposite direction (reverse bias). They act like one-way valves for electricity.

While resistance depends on a component's specific dimensions (length and cross-sectional area), resistivity is an intrinsic property of the material itself. It tells us how inherently good or bad a material is at conducting electricity, regardless of its shape or size. Think of it as a fingerprint for a material's electrical behaviour.

$\rho = \frac{RA}{L}$

The formula $\rho = \frac{RA}{L}$ can be rearranged to find the resistance of a specific wire or component if you know its material's resistivity, its length, and its cross-sectional area: $R = \frac{\rho L}{A}$. This is vital for designing circuits and selecting appropriate wires.

Thermistors are semiconductor devices whose resistance changes significantly with temperature. Unlike metals, most common thermistors (NTC - Negative Temperature Coefficient) experience a decrease in resistance as their temperature increases. This is because higher temperatures free more charge carriers, increasing conductivity.

Light-Dependent Resistors (LDRs) are semiconductor components whose resistance is influenced by light intensity. When exposed to brighter light, more electrons are excited and become free charge carriers, causing the LDR's resistance to decrease.

Superconductors are extraordinary materials that exhibit absolutely zero electrical resistivity when cooled below a specific, material-dependent critical temperature. This means current can flow indefinitely without any energy loss due to resistance. While most have very low critical temperatures, research continues to find higher temperature superconductors.

When we analyse circuits, we often consider ideal measuring instruments to simplify calculations and understand their purpose. These ideals represent the perfect scenario for measurement.