Power and Brightness of a Tungsten Filament
A tungsten filament at room temperature is connected to an ideal battery. Its temperature increases. What do EACH of the following do?
A tungsten filament at room temperature is connected to an ideal battery. Its temperature increases. What do EACH of the following do?
Resistance, current, power, and brightness
Resistance, current, power, and brightness
A) increases
A) increases
B) remains the same
B) remains the same
C) decreases
C) decreases
D) depends
D) depends
Solution: A, C, D, A
Solution: A, C, D, A
Resistivity (and thus resistance) of most materials (including tungsten) increases with temperature.
Resistivity (and thus resistance) of most materials (including tungsten) increases with temperature.
By Ohm's law, current must decrease.
By Ohm's law, current must decrease.
The power (defined as the rate of transformation of electrical to thermal energy) can be determined using P = (ΔV)2/R. As the resistance increases and the electric potential difference remains constant, the power decreases.
The power (defined as the rate of transformation of electrical to thermal energy) can be determined using P = (ΔV)2/R. As the resistance increases and the electric potential difference remains constant, the power decreases.
The power (defined as the rate at which thermal energy is transformed into visible light) is different. The Stefan-Boltzmann law describes the relationship between temperature and this power. A higher temperature corresponds to a higher overall light output. Some of this light is invisible, but a higher temperature object emits more light at all wavelengths. So the hotter tungsten emits more visible light and is therefore brighter.
The power (defined as the rate at which thermal energy is transformed into visible light) is different. The Stefan-Boltzmann law describes the relationship between temperature and this power. A higher temperature corresponds to a higher overall light output. Some of this light is invisible, but a higher temperature object emits more light at all wavelengths. So the hotter tungsten emits more visible light and is therefore brighter.
Note that the definition of power depends on the context. Any energy transfer or transformation can be in the numerator, so you need to be careful when using the term or the formula.
Note that the definition of power depends on the context. Any energy transfer or transformation can be in the numerator, so you need to be careful when using the term or the formula.