sketch the I–V characteristics of a metallic conductor at constant temperature, a semiconductor diode and a filament lamp

Resistance and Resistivity

In this lesson we will look at how current (I) varies with voltage (V) for three different kinds of conductors. We’ll use simple analogies and colourful boxes to keep the ideas clear.

1️⃣ Metallic Conductor (constant temperature)

Think of a metallic wire as a straight pipe that lets water (electric charge) flow through it. The pipe has a fixed resistance, so the amount of water that flows is directly proportional to the pressure (voltage) applied.

Mathematically:

\$V = IR\$  → \$ I = \dfrac{V}{R}\$

Voltage (V)Current (I)
00
10.5
21.0
31.5

Exam Tip: Remember that for a metal at constant temperature, the I–V curve is a straight line through the origin. If you’re given a point on the graph, you can find the resistance as the slope \$R = \dfrac{V}{I}\$.

2️⃣ Semiconductor Diode (p‑n junction)

Imagine a one‑way valve that only lets water flow in one direction. A diode behaves similarly: it conducts strongly in the forward direction but blocks current in reverse.

Its I–V relationship is exponential:

\$I = I_s \left(e^{\frac{qV}{kT}} - 1\right)\$

Voltage (V)Current (I)
-0.5≈0
0≈0
0.20.01
0.40.1
0.61.0

Exam Tip: When a diode is forward‑biased (positive voltage), the current rises steeply. In reverse bias, the current is almost zero until breakdown. Look for the “knee” of the curve in questions.

3️⃣ Filament Lamp (incandescent bulb)

Picture a metal wire that gets hotter as more water flows through it, making the pipe narrower (higher resistance). A filament lamp behaves like that: as voltage increases, the filament heats up, its resistance rises, and the I–V curve bends upward.

Approximate relationship:

\$R(T) = R0 \left(1 + \alpha (T - T0)\right)\$

with \$T\$ increasing as \$I\$ increases.

Voltage (V)Current (I)
00
20.4
30.8
41.4
52.2

Exam Tip: The filament lamp’s I–V curve is not a straight line. If you’re asked to find the resistance at a certain voltage, remember that the resistance is higher at higher temperatures, so you cannot use a single R value for all points.

Key Take‑aways

  1. Metallic conductors: linear I–V, constant resistance.

  2. Diodes: exponential I–V, one‑way conduction.

  3. Filament lamps: non‑linear I–V, resistance rises with temperature.

Use these analogies and tables to visualise how current behaves in different devices. Good luck with your studies! 🚀