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Homework Statement
. (a) It was pointed out in Section 15.3 that the temperature sensitivity of conductivity in semiconductors make them superior to traditional thermocouples for certain high-precision temperature measurements. Such devices are referred to as thermistors. As a simple example, consider a wire of 0.5 mm in diameter × 10 mm long made of intrinsic silicon. If the resistance of the wire can be measured to within 10^-3 Ω, calculate the temperature sensitivity of this device at 300 K. (hint: The very small differences here may make you want to develop an expression for dσ/dT.)
Homework Equations
The Attempt at a Solution
I know the equation relating temperature and conductivity is
σ=σ_0e^(-E_g/2kT)
So I integrate the formula to get dσ/dT = [σ_0(E_g/2k)e^(-E_g/2kT)]/T^2
and I know the formula for conductivity
σ=l/RA
where l is the length, R resistance, and A area.
My problem is that I don't know how to relate resistance sensitivity to temperature sensitivity