Answer:
The resistance of the Tungsten filament is 1352.8 Ohms
Explanation:
The temperature dependent value of resistance at any given temperature is given by the formula:
[tex]R = R_{ref}[1+ \alpha(T-T_{ref} )][/tex]
where
R = resistance of conductor at temperature T
R =[tex]\frac{V^{2} }{Power} =\frac{125^{2} }{7.5} = 2083.333\Omega[/tex]
[tex]R_{ref}[/tex] = resistance of conductor at reference temperature (20 degrees C)
T = Temperature of conductor = [tex]7\times 20 = 140C[/tex]
[tex]T_{ref}[/tex] = Reference Temperature [tex](20C)[/tex]
In the question, we are asked to find [tex]R_{ref}[/tex] which can be got by making it the subject of the formula as shown below:
[tex]R_{ref} =\frac{R}{[1+ \alpha(T-T_{ref} )]}[/tex]
[tex]R_{ref} =\frac{2083.333}{[1+0.0045(140-20 )]}= 1352.79\Omega[/tex]
∴The resistance of the filament at room temperature = 1352.8 Ohms
