Resistance

This page introduces resistance as the ratio of potential difference to current and relates it to material properties, dimensions, and temperature.

Definition

*️⃣ Resistance is defined as the ratio of potential difference to current.

In symbols, $$R = \dfrac{V}{I}$$ and it is measured in ohms (\(\Omega\)), with \(1\,\Omega = 1\,\mathrm{V\,A^{-1}}\).

Factor Affecting Resistance

The resistance of a uniform wire depends on its length \(L\), cross‑sectional area \(A\), and the material’s resistivity \(\rho\). For a wire of length \(L\) and cross‑sectional area \(A\), $$R = \dfrac{\rho L}{A}$$

Doubling the length doubles the resistance, while doubling the area halves it. For circular wires, \(A = \pi r^2\), so doubling the diameter significantly decreases the resistance by a factor of 4.

Effect of Temperature

For metallic conductors, resistivity and hence, resistance increases with temperature. As temperature rises, lattice vibrations increase and electron scattering becomes more frequent, producing a higher effective resistance (positive temperature coefficient).

Metal Lattice Simulation

3.0 V
20 °C
Mean drift speed: 0.0 mm/s
Resistance: Ω
At low temperature, ions vibrate less, so collisions are fewer and drift speed (and current) is higher for 3.0 V.
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I-V Characteristic Graphs

Ohmic Conductor I–V

An ohmic conductor obeys Ohm’s law at constant temperature: \(V \propto I\). Its I–V graph is a straight line through the origin and the resistance \(R = V/I\) (the slope) is constant.

Straight line through the origin: constant resistance, \(V \propto I\).

Filament Lamp I–V

The filament is a metal (typically tungsten) with a positive temperature coefficient of resistivity. As current flows, the filament heats up. Higher temperature increases lattice vibrations. Electrons scatter more, their mobility drops, and resistivity rises.

Curve bends so gradient decreases: resistance rises with current (heating).

Semiconductor Diode

A diode allows current to flow primarily in one direction: it conducts after a forward threshold and blocks in reverse (apart from a tiny leakage). Applications include rectifiers in power supplies, polarity protection, signal detection, and light emission in LEDs (special diodes that emit light under forward bias).

Diode Circuit Simulation

3.0 V
1.0 kΩ
I: 0.00 mA, emf: 3.0 V

A diode allows current to flow primarily in one direction: it conducts after a forward threshold and blocks in reverse (apart from a tiny leakage).

Very small current until threshold; steep rise after the knee; tiny reverse leakage.