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teb9186
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Here's the problem:
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?
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?