Resistance is defined as the measure of the opposition to current flow in an electrical circuit.
It is measured in ohms, symbolized by the Greek letter omega $(\ohm)$. All materials resist current flow to some degree. They fall into one of two broad categories: conductors and insulators.
Conductors are materials that offer very little resistance where electrons can move quickly. Examples of conductors are silver, copper, gold, and aluminum. Electrical wires contain conductors, which are primarily used to transport electricity from one point to another.
Insulators are materials that present high resistance and restrict the flow of electrons. Examples would include rubber, paper, glass, wood, and plastic. The common application of insulators is to provide outer covering to conductors in a wire.
Relationship of Resistance, Length and Area
To understand how we can solve the resistance of a given material through its physical properties, imagine water flowing through a tube; the wider the tube’s cross-sectional area, the more freely the water can flow. Additionally, the longer the tube is, the longer the time required for the water to pass through it.
Similarly, with a wire, its resistance can be determined as a function of its length and area. The resistance varies proportionally with its length and inversely with its area. Consequently, the longer the wire, the higher the resistance. On the other hand, the larger the area of the material, the lesser its resistance.
Mathematically, we can express it as:
\[R \propto \frac{L}{A}\]Hence, by multiplying a proportianality constant “$\rho$’’ we will get,
$$\begin{align} R = \rho\,\frac{L}{A} \label{eq:resistance using resistivity length and area} \end{align}$$
\(\begin{align*} \text{Where:}\quad R &= \text{resistance},\, [\mathrm{\ohm}] & \\ \rho &= \text{resistivity},\,[\mathrm{\ohm\cdot m}] \\ L &= \text{length},\,[\mathrm{m}] \\ A &= \text{area},\,[\mathrm{m^2}] \end{align*}\)