Question

Suppose you have 2 filament lamps which each have a resistance of 1 ohm and each need 3V.. If you connect them in parallel with each other and a 6V supply, you will get a current of 12A in the whole circuit and 6A to each lamp, because combined resistance would be only 0.5 Ohms. But, because the current to each lamp is high, wouldn't the resistance of the filament lamp increase(because of temperature), reducing current again? So will the resistance of the lamp keep increasing till current is 0?

When I say current is high, I mean higher than if we connected everything in series.

Answer 1

Filament lamps in parallel on a 6V supply will experience an initial current surge, but their resistance will increase as they heat up, stabilizing at a new equilibrium point and not continually increasing to zero.

Step-by-step explanation:

When two filament lamps with a resistance of 1 ohm, designed to operate at 3V each, are connected in parallel to a 6V supply, the initial assumption might be that the total resistance is halved to 0.5 Ohms, thus drawing 12A total and 6A to each lamp.

However, as the current through the filament lamps increases, the temperature of the filaments also rises. This, in turn, causes the resistance of the filament to increase as well due to the temperature coefficient of resistivity.

The resistance of the lamps does not increase indefinitely; it will stabilize at a higher value once the filament reaches its operating temperature. While the increased resistance does reduce the current slightly, it does not continue increasing to the point where the current reaches zero.

Instead, a new equilibrium is reached where the temperature-dependent resistance and the current through the lamps balance out. The behavior of the filament lamps’ resistance and current ultimately conforms to Ohm's law and the power equation (P = IV), taking into account that resistance is not constant but varies with temperature.