Answer:
1321.57 °C
Explanation:
Using,
R = R'[1+α(T-T')]....................... Equation 1
Where R = final resistance of the tungsten filament, R' = Initial resistance of the tungsten filament, T = Final Temperature, T' = Initial temperature, α = Temperature coefficient of tungsten filament.
Make T the subject of the equation,
T = [(R-R')/R'α]+T'.................... Equation 2
Given: R = 146 Ω, T' = 21.7 Ω, T = 20 °C,
Constant: α = 0.004403/°C
Substitute into equation 2
T = [(146-21.7)/(21.7×0.004403)]+20
T = (124.3/0.0955)+20
T = 1321.57 °C
The temperature of the hot tungsten filament is;
T = 1292.91 °C
The formula for resistance at a temperature T of the hot filament is;
R(T) = R_o(1 + α(T - T_o))
Where;
R(T) = resistance at temperature T
R_o = resistance at temperature To
T_o = Temperature when cold
T is temperature when hot
α is temperature coefficient of resistance
We are given;
R_o = 21.7 Ω
T_o = 20°C
R(T) = 146 Ω
α for tungsten filament online is 0.0045 /°C
Thus;
146 = 21.7(1 + 0.0045(T - 20))
146/21.7 = (1 + 0.0045(T - 20))
6.72811 - 1 = 0.0045T - 0.09
0.0045T = 5.72811 + 0.09
0.0045T = 5.81811
T = 5.81811/0.0045
T = 1292.91 °C
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