explain that the resistance of a filament lamp increases as current increases because its temperature increases

Resistance and Resistivity

How a filament lamp works

Inside a typical incandescent bulb, a thin tungsten filament is connected to two leads. When you switch the lamp on, electrons flow through the filament, creating a current. The filament resists this flow, so it heats up and emits light.

• ⚡️ Current (I) pushes electrons through the filament.
• 🔥 Heat (T) builds up because the filament resists the flow.
• 💡 Light is produced when the filament is hot enough.

Temperature dependence of resistance

The resistance of a conductor is given by

\$R = \rho \dfrac{L}{A}\$

where \$\rho\$ is the resistivity, \$L\$ is the length, and \$A\$ is the cross‑sectional area. For most metals, resistivity increases with temperature:

\$\rho(T) = \rho0 [1 + \alpha (T - T0)]\$

Here \$\alpha\$ is the temperature coefficient (≈ 0.004 /°C for tungsten). As the filament heats up, \$\rho\$ rises, so \$R\$ increases.

Think of it like this: traffic on a road. When the road is cool, cars (electrons) move easily. As the road heats up (traffic jam), cars slow down and the flow (current) becomes harder, increasing the “resistance” of the road.

Why does resistance increase as current increases?

1. Switch on the lamp → current starts flowing.
2. Current causes Joule heating in the filament: \$P = I^2 R\$.
3. Heat raises the filament temperature \$T\$.
4. Higher \$T\$ increases resistivity \$\rho\$ (and thus resistance \$R\$).
5. With higher \$R\$, the same applied voltage now drives a smaller current, so the heating effect stabilises.

In short, the filament’s resistance self‑regulates: more current → more heat → higher resistance → less current.

Illustrative table