Respuesta :
ANSWER
2020°C
EXPLANATION
Given:
• The initial resistance of the light bulb, R₀ = 20.0 Ω
,• The initial temperature of the filament of the light bulb, T₀ = 20°C
,• The final resistance of the fi light bulb when it is on, R = 160 Ω
,• The temperature coefficient of resistivity, α = 3.50 * 10⁻³ °C⁻¹
Unknown:
• The final temperature of the filament of the light bulb when it is on, T
The resistance and the change in temperature of a resistive element is given by,
[tex]R=R_o\lbrack1+\alpha(T-T_o)_{}\rbrack[/tex]We have to solve this equation for T. First, divide both sides by R₀,
[tex]\frac{R}{R_o}=1+\alpha(T-T_o)[/tex]Subtract 1 from both sides,
[tex]\frac{R}{R_o}-1=\alpha(T-T_o)[/tex]Divide both sides by α,
[tex]\frac{\frac{R}{R_o}-1}{\alpha}=T-T_o[/tex]And add T₀ to both sides,
[tex]T=\frac{\frac{R}{R_o}-1}{\alpha}+T_o[/tex]Replace with the known values and solve,
[tex]T=\frac{\frac{160\Omega}{20\Omega_{}}-1}{3.5\cdot10^{-3}\frac{1}{\degree C}}+20\degree C=\frac{8-1}{3.5\cdot10^{-3}\frac{1}{\degree C}}+20\degree C=\frac{7}{3.5\cdot10^{-3}\frac{1}{\degree C}}+20\degree C=2000\degree C+20\degree C=2020\degree C_{}[/tex]Hence, the temperature of the filament of the light bulb when it is on is 2020°C.
