Introduction to Electric Circuits

10.2 Dual circuits 237

'T

G

(a)

l

TC ,,, L

G

I J

IT c l L

(b)

Figure 10.5

'T L H

1

L

(c)

(c) This circuit shows an ideal transformer whose secondary winding is open

circuited and whose primary winding is fed from a voltage source. The

dual circuit will have the primary winding fed from a current source and

its secondary winding will be on short circuit. This is shown in Fig. 10.5(c).

Notice that, whereas the ultimate disaster in the circuit of Fig. 10.4(c)

would be a short circuited secondary winding leading to infinite current,

the corresponding catastrophe for the transformer in the dual circuit of

Fig. 10.5(c) would be an open circuited secondary winding leading to

infinite voltage.

A summary of the dual pairs associated with electric circuits is given in Table

10.2.

It must be emphasized that dual circuits are not equivalent circuits. Their

usefulness lies in modelling of systems. For example, it is much easier to obtain

a capacitor with a leakage resistance tending to infinity than it is to obtain an

inductor with a resistance tending to zero. In modelling systems having

inductors, therefore, dual circuits can be used to represent the 'real' system.

Table 10.2
Circuit statement Dual
Series
Series impedances are added
Open circuit
Switch open
Node
KCL
Thevenin's theorem
Nodal voltage analysis

Parallel

Parallel admittances are added

Short circuit

Switch closed

Loop/mesh

KVL

Norton's theorem

Mesh current analysis