Published by Patrick Mutisya · 14 days ago
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\$.