0195136047.pdf

2.1 THÉVENIN AND NORTON EQUIVALENT CIRCUITS 69

(a) KVL: 144− 24 IL− 48 IL− 96 =0, or 72IL=48, orIL=^2 / 3 A

Voc= 144 − 24 (^2 / 3 )=128 V

Deactivating or zeroing all ideal sources, i.e., replacing voltage sources by short

circuits in the present case, the circuit of Figure E2.1.1(b) reduces to that shown in

Figure E2.1.1(c).

Viewed from terminalsa–b, the 48-resistor and the 24-resistor are in parallel,

RTh= 48 ‖ 24 =

48 × 24

48 + 24

= 16 

Thus, the Thévenin equivalent to the left of terminalsa–b, attached with the 16-resistor,

is shown in Figure E2.1.1(d). Note that the Th ́evenin equivalent of any linear circuit

consists of a single Th ́evenin voltage source in series with a single equivalent Thevenin ́

resistance.

The current in the 16-resistor to the right of terminalsa–bcan now be found,

I= 128 / 32 =4A

(b) The 96-V source with 48in series can be replaced by a current source of 96/ 48 = 2

A with a parallel resistance of 48. Thus, by using source transformation, in terms

of current sources, the equivalent circuit to the left of terminalsa–bis given in Figure

E2.1.1(e).

Shorting terminalsa–b, one can findIsc,Isc=8 A. Replacing current sources by

open circuits, viewed from terminalsa–b,RTh= 48 ‖ 24 = 16 , which is the same as in

part (a). The circuit of Figure E2.1.1(e) to the left of terminalsa–breduces to that shown

in Figure E2.1.1(f).

Thus, the Norton equivalent to the left of terminalsa–b,attached with the 16-

resistor, is given in Figure E2.1.1(g). Note that the Norton equivalent of any linear

circuit consists of a single current source in parallel with a single equivalent Thevenin ́

resistance.

The current in the 16-resistor to the right of terminalsa–bcan now be found.I=4A,

which is the same as in part (a).

The equivalent source resistance, also known as the output resistance, is the same as the load

resistance of 16in the present case. Hence, resistance matching is accomplished for maximum

power transfer.

EXAMPLE 2.1.2

Consider the circuit of Figure E2.1.2(a), including a dependent source. Obtain the Thévenin
equivalent at terminalsa–b.