The potential difference across the filament of a lamp is...

The potential difference across the filament of a lamp is maintained at a constant level while equilibrium temperature is being reached. It is observed that the steady-state current in the lamp is only one tenth of the current drawn by the lamp when it is first turned on. If the temperature coefficient of resistivity for the lamp at $20.0^{\circ} \mathrm{C}$ is $0.00450\left(^{\circ} \mathrm{C}\right)^{-1},$ and if the resistance increases linearly with increasing temperature, what is the final operating temperature of the filament?

Key Concepts

Ohm's Law

Ohm's Law is a fundamental principle in electrical circuits that relates voltage, current, and resistance through the equation V = IR. It provides the framework for understanding how changes in resistance, due to temperature variations for instance, will influence the current when the voltage across a component remains constant.

Steady-State and Transient Conditions

This concept differentiates between the initial conditions of a system and its long-term behavior. In electrical circuits, when a device like a lightbulb is first switched on, it exhibits transient behavior—often a higher current because the initial resistance is lower. As heat builds up, the system settles into a steady state where parameters like current and resistance become constant. This distinction is essential in understanding dynamic changes in circuit parameters over time.

Resistance and Temperature Relationship

In many conductors, especially metals, resistance increases approximately linearly with temperature over a certain range. Understanding this relationship is key when analyzing devices such as lightbulb filaments, where the electrical resistance changes as the temperature rises, directly affecting the current in the circuit.

Temperature Coefficient of Resistivity

This concept describes how the resistivity of a material changes with temperature. It is particularly important in materials like metals where the resistivity typically increases as temperature rises. The coefficient quantifies the relative change per degree, allowing one to predict how the resistance of a conductor will change when its temperature is altered.

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