Yay calculus?
Man, I really shouldn't enhance my homework experience by making boring questions more "interesting..."
Like, for example, I just had to do the following problem:
A 50 kW, 120V, long-shunt compound generator is supplying a load at its maximum efficiency and the rated voltage. The armature resistance is 50 mΩ, series field resistance is 20 mΩ, shunt field resistance is 40 Ω, and rotational loss is 2 kW. What is the maximum efficiency of the generator?
It was easy to assume at first that maximum efficiency occurred at the rated load of the generator, but I quickly disproved that by counterexample. Then I had to come up with an expression for the efficiency in terms of the load... and instead of taking the rotational losses to be constant, I assumed that they varied linearly with the load on the machine: from 0 kW at zero load to 2 kW at the full load of 50 kW. Then I got to take the derivative of the whole expression, find the zeroes, and find the efficiency at the maximum point.
Also: OpenOffice Calculator doesn't like doing operations on complex numbers. Boo urns. I may have to turn to Matlab :\
Back to work now.
Like, for example, I just had to do the following problem:
A 50 kW, 120V, long-shunt compound generator is supplying a load at its maximum efficiency and the rated voltage. The armature resistance is 50 mΩ, series field resistance is 20 mΩ, shunt field resistance is 40 Ω, and rotational loss is 2 kW. What is the maximum efficiency of the generator?
It was easy to assume at first that maximum efficiency occurred at the rated load of the generator, but I quickly disproved that by counterexample. Then I had to come up with an expression for the efficiency in terms of the load... and instead of taking the rotational losses to be constant, I assumed that they varied linearly with the load on the machine: from 0 kW at zero load to 2 kW at the full load of 50 kW. Then I got to take the derivative of the whole expression, find the zeroes, and find the efficiency at the maximum point.
Also: OpenOffice Calculator doesn't like doing operations on complex numbers. Boo urns. I may have to turn to Matlab :\
Back to work now.