NEWBvU said:I don't see P (power) in your relevant equations ?
And what is R ? IF it's the resistance, how could that vary with V ?
You sure the exercise says ##V^5## and means applied voltage ?
I=dq/dt and Q=mcT are equations alright, and I can guess what the symbols stand for, but are they relevant equations ?
OH SORRY! i didnt copy it well. It meant P^5 proportional to V^8 sorry about thatBvU said:Link says ##V^{1.6}##.
And this is assuming changes in ##V## at normal operating conditions -- something the exercise should have mentioned too !
Usually we state ##P = V I = V^2/R##. So if ##R## is constant, we have ##P\propto V^2##. To get ##\propto V^5## you would need ##R\propto V^{-3}## which to me seems mission impossible.
The power on the tungsten filament in a light bulb is mainly dissipated by radiation. How does the radiated power depend on temperature (think of black-body radiation).rohanlol7 said:OH SORRY! i didnt copy it well. It meant P^5 proportional to V^8 sorry about that
So okay. ill try using stefan Boltzmann lawehild said:The power on the tungsten filament in a light bulb is mainly dissipated by radiation. How does the radiated power depend on temperature (think of black-body radiation).
T= temperataure of filament Ti=temperature outside k,m,a are constantsehild said:The power on the tungsten filament in a light bulb is mainly dissipated by radiation. How does the radiated power depend on temperature (think of black-body radiation).
No, that is not true.rohanlol7 said:T= temperataure of filament Ti=temperature outside k,m,a are constants
So the temperature is proportional to the Power disspated.
The filament is much hotter than the surroundings, (about 2500 °C) so you can ignore Ti. And change the minus to plus. Approximately, the resistance is proportional to T.rohanlol7 said:P=m(T^4-Ti^4)=mT^4 ( approximately)
Resistance of the filament lamp =R=Ro(1+a(T-Ti))
Considering the lamp with current I through it V=I*Ro(1-a(T-Ti))=IRo(1-aT) (approximately)
From there I can't quite continue
your equation for resistance variation with temperature for a metal is wrong. The resistance increases with temperature and the variation with temperature is only linear for 'low' temperatures. The temperature of a tungsten filament bulb would not be considered as 'low'rohanlol7 said:T= temperataure of filament Ti=temperature outside k,m,a are constants
So the temperature is proportional to the Power disspated. T=kP. P=m(T^4-Ti^4)=mT^4 ( approximately)
Resistance of the filament lamp =R=Ro(1-a(T-Ti))
Considering the lamp with current I through it V=I*Ro(1-a(T-Ti))=IRo(1-aT) (approximately)
From there I can't quite continue
The filament lamp model is a theoretical model that explains the relationship between temperature and resistance in a light bulb. It states that as the temperature of the filament increases, the resistance also increases, leading to a decrease in current and ultimately the production of light.
The filament lamp model is derived using the Stefan-Boltzmann law, which relates the temperature of a blackbody (such as the filament in a light bulb) to the rate at which it emits thermal radiation. This is combined with Ohm's law, which describes the relationship between current, voltage, and resistance, to create a mathematical model for the behavior of the filament in a light bulb.
The filament lamp model makes several simplifying assumptions, including that the filament behaves as a blackbody, that the resistance of the filament is proportional to its temperature, and that the temperature of the filament is uniform along its length.
The filament lamp model is a simplified theoretical model and may not accurately reflect the behavior of a real light bulb. Factors such as the composition of the filament and the surrounding gas can affect the accuracy of the model. However, it provides a good approximation for understanding the general behavior of a light bulb.
The filament lamp model is used in the design and optimization of light bulbs, as well as in the study of thermodynamics and electrical circuits. It also has applications in areas such as materials science and engineering, where the behavior of high-temperature materials is of interest.