%3Cp%3E%3Cspan%20class%3D%22c1%22%3E1)%20A.%20Two%20conductors%20are%20made%20of
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%3Cp%3E%3Cspan%20class%3D%22c1%22%3E1)%20A.%20Two%20conductors%20are%20made%20of%20the%20same%0Amaterial%20and%20have%20the%20same%20length.%20Conductor%20%3C%2Fspan%3E%3Ci%20class%3D%0A%22c2%22%3EA%3C%2Fi%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Bis%20a%20solid%20wire%20of%0Adiameter%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c3%22%3E2.0%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c1%22%3E%26nbsp%3Bmm.%20Conductor%26nbsp%3B%3C%2Fspan%3E%3Ci%20class%3D%0A%22c2%22%3EB%3C%2Fi%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Bis%20a%20hollow%20tube%20of%20outside%0Adiameter%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c3%22%3E6.0%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c1%22%3E%26nbsp%3Bmm%20and%20inside%20diameter%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c3%22%3E3.0%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3E%26nbsp%3Bmm.%20What%20is%20the%20resistance%0Aratio%26nbsp%3B%3C%2Fspan%3E%3Ci%20class%3D%0A%22c2%22%3ER%3Csub%3EA%3C%2Fsub%3E%2FR%3Csub%3EB%3C%2Fsub%3E%3C%2Fi%3E%3Cspan%20class%3D%22c1%22%3E%2C%20measured%0Abetween%20their%20ends%3F%26nbsp%3B%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3E____%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3E%3Cbr%20%2F%3E%3C%2Fspan%3E%3C%2Fp%3E%0A%3Cp%3E%3Cspan%20class%3D%22c1%22%3E2.%20A%20common%20flashlight%20bulb%20is%20rated%20at%200.30%20A%0Aand%26nbsp%3B%3C%2Fspan%3E2.9%3Cspan%20class%3D%22c1%22%3E%26nbsp%3BV%20(the%20values%20of%20the%0Acurrent%20and%20voltage%20under%20operating%20conditions).%20If%20the%20resistance%0Aof%20the%20bulb%20filament%20at%20room%20temperature%20(20%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c4%22%3E%C2%B0%3C%2Fspan%3E%3Cspan%20class%3D%22c1%22%3EC)%20is%26nbsp%3B%3C%2Fspan%3E1.0%3Cspan%20class%3D%0A%22c1%22%3E%26nbsp%3B%3C%2Fspan%3E%3Cimg%20src%3D%0A%22http%3A%2F%2Fwww.webassign.net%2Fimages%2Fomegacap.gif%22%20class%3D%0A%22c5%22%20%2F%3E%3Cspan%20class%3D%22c1%22%3E%2C%20what%20is%20the%20temperature%20of%20the%20filament%0Awhen%20the%20bulb%20is%20on%3F%20The%20filament%20is%20made%20of%0Atungsten.%3C%2Fspan%3E%3Cbr%20class%3D%22c6%22%20%2F%3E%0A%3Cspan%20class%3D%22qTextField%20c1%22%3E%3Cinput%20type%3D%22text%22%20name%3D%0A%22RN_776102_3_0_781883%22%20value%3D%22%22%20size%3D%2210%22%20id%3D%22RN_776102_3_0_781883%22%0Adir%3D%22ltr%22%20class%3D%22c7%22%20%2F%3E%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c1%22%3E%26nbsp%3B%3C%2Fspan%3E%3Cspan%20class%3D%22c4%22%3E%C2%B0%3C%2Fspan%3E%3Cspan%20class%3D%0A%22c1%22%3EC%3C%2Fspan%3E%3C%2Fp%3E%0AExplanation / Answer
Calculate the resistance when the bulb is in operation, as per the resistance definition:
R = V/I
Resistivity varies with temperature as such:
rho = rho0 + alpha*(T - T0)
where rho0 is the resisitivity at T0, alpha is the temperature coefficient of resistivity, T is the operation temperature, and rho is the operation resistivity.
Assuming the geometry is unchanged, resistance is proportional to resistivity. Thus:
R = R0 + alpha*(T - T0)
Substitute R:
V/I = R0 + alpha*(T - T0)
Solve for T:
T = T0 + (V/I - R0)/alpha
Data:
T0:=20 C; R0:=1 ohms; V:=2.9 Volts; I:=0.30 Amps; alpha:=0.0046 1/C;
Result:
T = 20 + (2.9/0.30 - 1)/(0.0046) = 1904 celsius = 2177 K
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