We know Joule’s heating effect –

Joule’s heating effect is the process by which the passage of an electric current through a conductor produces heat

When a constant potential difference is applied across a bulb, due to Joule’s heating effect, the temperature of the bulb increases.

We know in case of metals, the temperature co-efficient is positive, which means, with increase in temperature, the Resistance of the metal increases.

In case of metals, the resistance and temperature is related as -

Where,

R= resistance at some temperature T

R₀ = resistance at zero temperature

and = Temperature co-efficient.

From ohm’s law

Voltage,

Where

I is the current

R is the resistance

Thus, from the above formula, we get that with increase in resistance, current decreases. if the voltage remains constant

Now, the heat generated by the resistance is constantly radiated through the connecting wires into the surroundings.

Thus, the value of its temperature is maintained constant and so its resistance.

As a result, the current through the bulb filament becomes constant.