The resistance of the tungsten filament in a light bulb changes with temperature according to equation (1), below.
I am supposed to calculate the temperature of the light bulb at voltage 0.8280 volts and a current of 0.0853 amps. The bulb is connected to a 1.5915 volt battery. The bulb's resistance is 2.28 ohms.
R = Ro(1+a(T-To))......................................(1)
T = (-1a^-1)+(a^-1)(Ro^-1)(R)+T................(2)
Where Ro is the resistance at the initial temperature To, and R is the resistance at the final temperature, T. a is the coefficient of resistivity.
The Attempt at a Solution
The coefficient of resistivity for tungsten is 0.0045 degrees Celsius ^-1.
I assumed To to be 20 degrees Celsius.
I assumed Ro to be 2.28 ohms, the resistance of the bulb alone.
I want to find T, but I didn't have R yet, so I calculated it with:
R = voltage across bulb (V) / current through bulb (A)
= 0.8280 V / 0.0853 A
= 9.71 ohms
I put my values for Ro, R, To, and a into equation (1). I got T = 20, the same as To, so I checked two different online equation solvers. They told me I had made a mistake in the calculation, and that T was actually 744 degrees Celsius. I checked this on equation (2) and got the same answer. I knew this couldn't be right, so I switched my values for R and Ro. The solver and equation (2) both had T = -147 degrees. This does not seem right.
My question is, where did I go wrong? I am sure that To and a are correct. I suspect I have the wrong R value. How can I find the correct value for R? Is Ro correct? Any help will be greatly appreciated. This is due on April 2, and it has me stumped.