0195136047.pdf

12.1 BASIC PRINCIPLES OF ELECTROMECHANICAL ENERGY CONVERSION 507

in principle and are magnetic-field devices.
Three basic principles associated with all electromagnetic devices are (1)induction,(2)
interaction,and (3)alignment.

Induction

The essentials for producing an emf by magnetic means are electric and magnetic circuits, mutually
interlinked. Figure 12.1.2(a) shows a load (or sink or motor) convention with the induced emf
(or back emf)edirected in opposition to the positive current, in which case Faraday’s law of
induction,

e=+

dλ

dt

=+N

dφ

dt

(12.1.2a)

applies, whereλis the flux linkages,Nis the number of turns, andφis the flux. On the other
hand, the induced emfe(or generated emf) acting in the direction of positive current, as shown
in Figure 12.1.2(b) with a source (or generator) convention, satisfies Faraday’s law of induction,

e=−

dλ

dt

=−N

dφ

dt

(12.1.2b)

The change in flux linkage in a coil may occur in one of the following three ways:

1. The coil remaining stationary with respect to the flux, the flux varies in magnitude with
   time. Since no motion is involved, no energy conversion takes place. Equation (12.1.2a)
   gives thetransformer emf(or thepulsational emf) as in the case of a transformer (see
   Chapter 11), in which a time-varying flux linking a stationary coil yields a time-varying
   voltage.


2. The flux remaining constant, the coil moves through it. A conductor or a coil moving
   through a magnetic field will have an induced voltage, known as themotional emf(or
   speed emf), given by

+

−

+

−

+

−

+

−

+

−

+

−

v

i R

e v

R i

+

−

e

v = Ri + e = Ri + =ddtλ Ri + Nddtφ

(a)

v

i R

e v

R i

+

−

e

v = e − iR = − ddtλ − iR = −N ddtφ− iR

(b)

Figure 12.1.2Circuit conven-

tions.(a)Load (or sink or motor)

convention. Note that the power

absorbedby the circuit is posi-

tive whenvandiare positive, and

when current flows in the direc-

tion of voltage drop.(b)Source

(or generator) convention. Note

that the powerdeliveredby this

circuit to the external circuit is

positive whenvandiare posi-

tive, and when current flows out

of the positive terminal.