To define electrical resistance and understand the variables that determine its value.
Electrical resistance ($R$) is a measure of how strongly a material opposes the flow of electric current. It quantifies the relationship between the potential difference ($V$) applied across a conductor and the resulting current ($I$) that flows through it.
Mathematically, resistance is defined by Ohm’s law:
$$R = \frac{V}{I}$$where:
The resistance of a uniform conductor depends on three main factors:
These factors are combined in the resistivity formula:
$$R = \rho \frac{L}{A}$$where $\rho$ is the resistivity of the material (Ω·m).
| Symbol | Quantity | Unit |
|---|---|---|
| $R$ | Resistance | Ω (ohm) |
| $V$ | Potential difference | V (volt) |
| $I$ | Current | A (ampere) |
| $\rho$ | Resistivity | Ω·m |
| $L$ | Length of conductor | m (metre) |
| $A$ | Cross‑sectional area | m² (square metre) |
Calculate the resistance of a copper wire 2.0 m long with a cross‑sectional area of $1.0 \times 10^{-6}\,\text{m}^2$. The resistivity of copper is $\rho = 1.68 \times 10^{-8}\,\Omega\!\cdot\!\text{m}$.
Using $R = \rho \dfrac{L}{A}$:
$$R = (1.68 \times 10^{-8}) \frac{2.0}{1.0 \times 10^{-6}} = 3.36 \times 10^{-2}\,\Omega$$The wire has a resistance of $0.0336\;\Omega$.