
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 0.80volt 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. 22 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) + (0j10) = 10j10 = 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)= 15j8.66=17.32v. 
11 
Two generators on the same shaft generate voltages E_{1} = 80 and E_{2} = 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. 
