Resistance of a Wire

Electrical resistance tells us how much a wire opposes the flow of electric charge. Think of charges like people moving through a corridor: a longer corridor with rough flooring slows them down more; a wider corridor lets more people through at once.

Key ideas

• Definition: Resistance $R$ measures how hard it is for current to flow. Units: ohms ($\Omega$).
• Ohm’s law (for a fixed temperature): $R = \dfrac{V}{I}$, where $V$ is voltage (volts) and $I$ is current (amperes).
• For a uniform metal wire: $$R \propto L, \quad R \propto \frac{1}{A}$$ Longer wire means larger resistance; greater cross-sectional area $A$ (thicker wire) means smaller resistance.
• Material matters: $R = \rho \dfrac{L}{A}$, where $\rho$ (rho) is the resistivity of the material. Nichrome and constantan have higher $\rho$ than copper.
• Temperature effect (metals): as temperature increases, resistance usually increases.

Length and thickness

A longer wire is like a longer corridor—more collisions slow charges, so $R$ increases with $L$. A thicker wire is like a wider doorway—more paths for charges, so $R$ decreases as $A$ increases. For round wire, $A = \pi r^2$ with $r = \dfrac{d}{2}$.

Measuring the resistance of a wire

1. Set up: power supply (low voltage), ammeter in series, voltmeter across the test length of wire on a ruler. Use short bursts of current to avoid heating.
2. Choose a length $L$ between two crocodile clips. Record $V$ and $I$. Calculate $R=V/I$.
3. Repeat for several lengths and plot $R$ against $L$. A straight line through the origin shows $R \propto L$. Keep the wire thickness and material the same.

Common misconceptions

• “Thicker wire has more resistance.” False—thicker means lower resistance.
• Ignoring heating—warming the wire can increase $R$ and change results.
• Measuring the whole coil length—only measure between the clips.