For a certain semiconductor material

MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

For a certain semiconductor material, the electrical resistance

R

(in ohms) varies with absolute temperature

T

(in kelvins) according to

R(T)=kT^{n},

where

k

is a positive constant and

n

is a real exponent (not necessarily an integer). (a) Write an expression for

R'(T)

in terms of

k

n

, and

T

. (b) Describe in words the physical meaning of

R'(T)

for this material. (c) Determine the units of

k

and of

R'(T)

, explaining your reasoning. (d) Suppose

0<n<1

. Explain qualitatively how the magnitude of

R'(T)

changes as

T

increases and discuss what this indicates about the material’s sensitivity to temperature at high versus low temperatures.