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An AC generator of rms voltage E is connected in series with two reactive impedances,
Z_1 and Z_2, as shown below:
\theta is the argument of Z_1 and \phi is the argument of Z_2.
Find the power dissipated in Z_2
If the phase of Z_2 (\phi) is fixed whilst allowing the magnitude to vary, find the relationship between Z_1 and Z_2 when we achieve maximum power transfer to Z_2.
If xyz = 1 and x+y+z =1/x + 1/y + 1/z show that at least one of these numbers must be 1. Now for the complexity! When are the other numbers real and when are they complex?
Show that x = 1 is a solution of the equation x^(3/2) - 8x^(-3/2) = 7 and find all other solutions.
This problem in geometry has been solved in no less than EIGHT ways by a pair of students. How would you solve it? How many of their solutions can you follow? How are they the same or different? Which do you like best?