Problems

Author: E.E. Kimberly

	Problem	Answer
1	A conductor in which the generated voltage is 0.80 volt (effective) is connected in series with a second conductor in which the generated voltage of the same frequency is 2.0 volts (effective), the second voltage being 30° out of phase with the first and lagging it in time. Calculate the resulting voltage appearing across the free ends of the two conductors	2.7 volts
2	Express as a complex quantity the sum of the two voltages of Problem 1, assuming the 0.80-volt vector to lie along the axis of reference.
3	Construct the sinusoids to represent the voltages of Problem 1.
4	Assume that on the rotating member of Fig. 2-2 there are eight conductors in the positions A, B, C, D, E, F, G, and H, respectively, at a given instant. Let the ends of the conductors away from the observer be designated by primes. Assume that every conductor generates a voltage of 10 volts rms and that its ends are connected through sliding brush contacts to a stationary terminal board. If A' were connected to C, what voltage would appear between A and C'?	14.14 volts
5	If, in Problem 4, A' were connected to C', what voltage would appear between A and C?	14.14 volts
6	If, in Problem 4, A' were connected to D, what voltage would appear between A and D'?	7.65 volts
7	If, in Problem 4, A' were connected to D' and D were connected to G, what voltage would appear between A and G'?	24.14 volts
8	How could all the conductors in Problem 4 be connected in series to produce the highest possible voltage at two external terminals? How much would this voltage be?	Connect A' to Ef, E to B, B' to F', F to H, Hf to D', D to C, C' to G'. Read 52.66 volts between A and G. Several other equivalent combinations are possible.
9	Assuming the voltage of conductor AA' in Problem 5 to lie along the axis of reference in a positive sense, show the addition of voltages in complex form. Use rms values.	(10+j0) + (0-j10) = 10-j10 = 14.14 v. or (10+j0) - (0+j10) = 10 -j10 = 14.14 v.
10	If, in Problem 4, A' were connected to D' and the conductor DD' were 120° ahead of conductor AA', what voltage would appear between A and D? Show the complex addition of voltages.	(10+j0]-(-5+j8.66)= 15-j8.66=17.32v.
11	Two generators on the same shaft generate voltages E1 = 80 and E2 = 60. There is a phase angle of 45 deg between the two voltages. Calculate the two voltages that could be obtained by connecting the two generators in series.