Understanding Current in Tungsten Filament Lamps

When a tungsten filament lamp is switched on, the current drawn is not constant. It changes from the moment the supply is connected until the lamp reaches its operating temperature. The question asks about the difference between the initial current and the steady-state current measured by an ammeter.

Let's analyze what happens inside a tungsten filament lamp.

Resistance and Temperature in Tungsten Lamps

The filament in the lamp is made of tungsten. Tungsten is a metal, and like most metals, its electrical resistance changes with temperature. Specifically, the resistance of tungsten increases significantly as its temperature increases. This property is crucial to understanding the current drawn by the lamp.

• When the lamp is cold (just switched on), the tungsten filament is at room temperature. Its resistance is relatively low.
• As current flows through the filament, it heats up rapidly due to the power dissipated (\(P = I^2 R\)).
• As the filament gets hotter and hotter, its resistance increases.
• Eventually, the filament reaches a very high temperature (around 2500-3000°C) and glows brightly. At this point, it reaches a steady-state temperature, and its resistance stabilizes.

Applying Ohm's Law to Lamp Current

Ohm's Law states that the current (\(I\)) flowing through a conductor is directly proportional to the voltage (\(V\)) across it and inversely proportional to its resistance (\(R\)), given by the formula: \(I = \frac{V}{R}\). Assuming the supply voltage \(V\) is constant, the current drawn by the lamp is determined by its resistance \(R\).

Based on Ohm's Law and the change in resistance:

• When the supply is switched on, the filament is cold, resistance is low, leading to a high initial current (often called an inrush current).
• As the filament heats up, resistance increases, causing the current to decrease.
• In the steady state, when the filament is hot and glowing brightly, the resistance is much higher than when it was cold. This results in a lower steady-state current.

Therefore, the ammeter reading when the supply is switched on will be higher than the ammeter reading under steady-state conditions.

The question asks about the ammeter reading under steady state condition compared to the ammeter reading when the supply is switched on. Since the steady-state current is lower than the initial current, the ammeter reading under steady state condition will be less than the ammeter reading when the supply is switched on.

Revision Table: Tungsten Filament Lamp Behavior

Additional Information: Temperature Coefficient of Resistance

The property of a material where its resistance changes with temperature is quantified by its temperature coefficient of resistance (\(\alpha\)). For most metals like tungsten, \(\alpha\) is positive, meaning resistance increases with increasing temperature. For some materials (like semiconductors), \(\alpha\) can be negative, meaning resistance decreases with increasing temperature.

The resistance \(R_T\) at a temperature \(T\) can be approximated by the formula:

\(R_T = R_0 [1 + \alpha (T - T_0)]\)

Where:

• \(R_T\) is the resistance at temperature \(T\).
• \(R_0\) is the resistance at a reference temperature \(T_0\) (e.g., room temperature).
• \(\alpha\) is the temperature coefficient of resistance of the material.
• \(T\) is the temperature of the material.
• \(T_0\) is the reference temperature.

For tungsten, \(\alpha\) is positive and relatively large, which is why the resistance changes so significantly between room temperature and operating temperature.