(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

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.

3. 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.

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# Resistance of a light bulb changing with temperature

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