Understanding Filament Lamp Resistance and Voltage

A filament lamp, also known as an incandescent light bulb, works by passing an electric current through a thin wire filament (typically made of tungsten). This current heats the filament to a very high temperature (around 2500 °C to 3000 °C), causing it to emit light.

The question asks what happens to the resistance of the lamp when it draws higher voltages. Let's consider the relationship between voltage, current, power, and temperature in a filament lamp.

According to Ohm's Law, the voltage (\(V\)) across a conductor is proportional to the current (\(I\)) flowing through it, provided the temperature remains constant. The resistance (\(R\)) is the constant of proportionality:

\(V = IR\)

Also, the power (\(P\)) dissipated by a resistor is given by:

\(P = VI = I^2R = \frac{V^2}{R}\)

When a higher voltage is applied across the filament lamp, a larger current flows through it (assuming the resistance doesn't change initially). This increased current leads to a significantly higher power dissipation in the filament. This can be seen from the power formulas; if V increases, P increases, and if I increases, P increases.

This increased power dissipation causes the temperature of the filament to rise considerably. Tungsten, like most metallic conductors, exhibits a property where its electrical resistance increases with increasing temperature.

Think of the free electrons moving through the metal lattice. As the temperature increases, the atoms in the lattice vibrate more vigorously. These vibrations obstruct the flow of electrons, making it harder for the current to pass through. This increased obstruction is what we observe as an increase in resistance.

Therefore, when the filament lamp draws higher voltages, the filament gets much hotter, and consequently, its resistance increases.

Step-by-Step Analysis

• Higher voltage is applied to the filament lamp.
• According to \(V=IR\), a higher voltage tends to cause a higher current.
• Higher current leads to increased power dissipation (\(P=I^2R\) or \(P=V^2/R\)).
• Increased power heats the filament to a higher temperature.
• For metallic conductors like the tungsten filament, resistance increases with temperature.
• Conclusion: Higher voltage leads to higher temperature, which leads to higher resistance.

Relationship Summary: Voltage, Temperature, and Resistance

This explains why the resistance of a filament lamp is not constant and increases significantly as it operates at higher voltages and reaches its intended operating temperature.

Revision Table: Key Concepts

Additional Information: Resistance and Temperature

For most metallic conductors within a certain temperature range, the resistance \(R\) varies approximately linearly with temperature \(T\) according to the formula:

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

Where:

• \(R(T)\) is the resistance at temperature \(T\).
• \(R_0\) is the reference resistance at a reference temperature \(T_0\) (often 0 °C or 20 °C).
• \(\alpha\) is the temperature coefficient of resistance for the material. For most metals like tungsten, \(\alpha\) is positive, meaning resistance increases with temperature.
• \((T - T_0)\) is the change in temperature.

Tungsten has a positive and relatively large temperature coefficient of resistance. Its resistance at operating temperature (around 2500-3000 °C) can be more than 10 times its resistance at room temperature.