Introduction to Electric Circuits

240 Duals and analogues

Applying KVL to the outer loop gives

11R1 = 12R2 (10.10)

Equation (10.10) could of course been obtained from Equations (10.8) and

(10.9) simply by equating their right-hand sides.

Applying KCL to node X gives

I = I~ + I2 (10.11)

By analogy, the equations for the magnetic circuit may now be written down

immediately. Thus, from Equation (10.8) we have

F(=N/) = q~S + q~2S2 (10.12)

From Equation (10.9) we see that

NI = ~S + @~S~ (10.13)

Equation (10.10) indicates that

q~,S, = q~zS2 (10.14)

Finally, by analogy with Equation (10.11), we have

q~ = q~, + q~2 (10.15)

Table 10.3 summarizes the analogies between the electric and magnetic fields.

Table 10.3

Electric Magnetic Conductive

Electric flux, ~ Magnetic flux, 9 Electric current, I

Field strength, E Field strength, H Field strength, E

Flux density, D Flux density, B Current density, J

Permittivity, e Permeability, ~ Conductivity, cr

Reluctance, S Resistance, R

mmf, F emf, E

Electrical and mechanical systems

Electric circuits are made up of energy sources, sinks and stores represented,

respectively, by voltage or current sources, resistors and inductors or capaci-

tors. Similarly, in mechanical systems there are sources of force, together with

energy sinks (for example, dashpots) and energy stores (for example, springs or

moving masses). There are analogous quantities in the two systems leading to

analogous equations. There are summarized in Table 10.4.

Since the form of the equations shown in the table is identical in both

systems, their manipulation is likewise identical.