Answer:
the question has a little typographical error. the complete question is If a certain silver wire has a resistance of 9.00 Ω at 30.0°c, what resistance will it have at 44.0°c?
The resistance of Silver is 9.48Ω
Explanation:
The resistivity of all materials depends on temperature. Equally, the resistivity of conductors increases with increasing temperature. Because the atoms in these conductors vibrate more rapidly and over larger distances at higher temperatures. The electrons making more collisions as they are moving through the metal, effectively making the resistivity higher. Over relatively small temperature changes (about 100C or less), resistivity ρ varies with temperature change ΔT as expressed in the following equation
ρ = ρ0 (1+ αΔT )………………..Equation 1
Where ρ0 is the original resistivity and α is the temperature coefficient of resistivity. For larger temperature changes, α may vary or a nonlinear equation may be needed to find ρ.
The resistance of an object also depends on temperature, since R0 is directly proportional to ρ. For a cylinder, we know R= ρL/A, and so, if L and A do not change greatly with temperature, R will have the same temperature dependence as ρ. Investigation of the coefficients of linear expansion prove them to be about two orders of magnitude less than typical temperature coefficients of resistivity, hence the effect of temperature on L and A is about two orders of magnitude less than on ρ.
Thus, R = R0 (1+ αΔT )……………………………..Equation 2
is the temperature dependence of the resistance of an object, where R0 is the original resistance and R is the resistance after a temperature change ΔT. The temperature coefficient of resistivity α per degree C of Silver is 0.0038
We are going to use equation 2 to solve the question by substituting the values of the R0, α, and ΔT.
R0 = 9Ω
α = 0.0034
ΔT = 44 – 30 = 14 C
R = 9 (1 + 0.0038*14) =9.48Ω
The resistance of Silver is 9.48Ω
