By Richard T. Smith (Auth.)

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5 (for the 2-winding case) in terms of the first equivalent circuit parameters, and turns ratio. 17. A transformer has three windings on the same core. Load impedance 3 + j4 is on winding 3; |/ | = 10; e, = 10/0°; /, = 3 0 / 3 0 ° ; #, = 100, and N =500. Find the phasor voltage and current of each winding. r 2 ? 18. For a certain electromagnet, the relation among current, plunger position, and flux linkages has been experimentally found to be where a, b, and d are positive constants. Derive an expression for the force applied to the plunger by the electrical system.

The other wave actually degrades the performance of the machine by producing an oscillatory torque. Stability of operation of this simple machine is also quite an interesting development. Consider first the case of dc current in winding s and no current in winding r. Then T =- L llsin20. e 2 When 0 = 0 there is no torque. However, if the rotor is displaced slightly from this position, a torque is developed which tends to restore the rotor to position 0 = 0 . In other words, 0 = 0 is a stable equilibrium position of the rotor.

16) are the equations we need to solve many problems involving the commutator machine. 1 Consider a dc machine with one set of brushes, in the g-axis, and only one other winding — / . Then the above equations reduce to, assuming steady state operation (all d/dt 's = 0, except pa = v — constant) (i) pfd (2) = ffd fd x L l +,= (3) fd= (4) e - ri + $ v. q (5) d The electrical power supplied to the machine is tfifd + q( e ~ 1 q) = ' fd + ( ~ Wfd l H q + V)( " * q) (*) The first two terms on the RHS of (7) are resistance losses.

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