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teb9186

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The temperature coefficient of resistivity alpha is given by alpha = dr/rdT where r is the resistivity at temperature T. From this expression follows r(T) = ro[1 + a(T - To)], if a is presumed to be constant and much smaller than (T - To)-1.

(a) (3 points) However, if a is not constant, but is given by alpha = -n/T, show that r = a/T^n^, where n is a dimensionless constant, r is given in W·m and T is given in kelvin (K). Such a relation might be used as a rough approximation for the current temperture dependence of the resistivity for a semiconductor.

(b) (1 point) Using the values r = 3.50 × 10-5 W·m and alpha = -5.00 × 10-4 K-1 for

graphite at 293 K, (note: the w's are ohm symbols)

determine a

The first thing I did was differentiated r(t) and divided that by r and set that equal to alpha. I got alpha=ro(T-To)/r since this equals -n/T i set the two equal and found that r=(-ro9T-To)T/n

I don't know how to get what I got for r into the form given. Can somebody help?

I also have this short circuit problem and I have no idea where to started:

A long underground cable with length L = 12.0 km extends east to west and it consists of two parallel wires, each of which has a linear resistivity rL = 10.0 W/km. A short develops at distance x from the west end when a conducting path of unknown resistance R connects the wires. (See the figure above.) The resistance of the wires and the short is then RE = 120 W when the measurement is made from the east end, and RW = 200 W when it is made from the west end.

(a) (4 points) Find x and R algebraically in terms of L and rL, RE and RW.

(b) (1 point) Evaluate your results numerically.

Again the w's are ohms

I have been trying different things but I am very confused. I don't understand how a short circuit would happen in this situation. Arent the two wires that are connected at the same potential, meaning know charge would flow between them?