Introduction to Electric Circuits

236 Duals and analogues

of a short circuit current in parallel with an admittance Ysc. The voltage across

the load admittance YL, connected across the load terminals A and B, is then

calculated from the equation

VL = Isc/(Ysc + YL) (10.4)

Notice the duality of Equations (10.3) and (10.4) and of the statements in the

above two paragraphs.

Open circuit and short circuit

It can be seen from the consideration of Thevenin's and Norton's theorems that

a short circuit is the dual of an open circuit.

Example 10.2

Obtain the duals of the circuits shown in Fig. 10.4.

R L C

l ; II

v()

(a)

v9

1

tL C

(b)

Figure 10.4

I.

v

[-

q^1

(c)

Solution

(a) The voltage source is replaced by a current source; the circuit consisting of
a resistor R, an inductor L and a capacitor C in series is replaced by one
consisting of a conductance G, a capacitor C and an inductor L in parallel.
This is shown in Fig. 10.5(a).
(b) The voltage source is replaced by a current source; the circuit consisting of
a series combination of a resistor R and an inductor L in parallel with a
capacitor C is replaced with one consisting of a parallel combination of a
conductance G and a capacitor C in series with an inductor L. This is
shown in Fig. 10.5(b).