Introduction to Electric Circuits

52 DC circuit analysis

I~ = Eo/(Ro + r)- 16.7/(23.33 + r) (3.11)

Ie is a maximum when r has its minimum value (i.e. 0 11):

&max -- 16.7/23.33 = 0.72 A

IL is a minimum when r has its maximum value (i.e. 250 f~):

ILmin = 16.7/(23.33 + 250) = 0.06 a

Using Thevenin's theorem the current Ie is now easily obtained for any value
of r simply by putting that value into Equation (3.11) above. Using Kirchhoff's
laws or the principle of superposition, we would have to rework the whole
problem for every value of r.

3.7 NORTON'S THEOREM

In 1926 Norton, an American engineer, introduced an equivalent circuit which
is the dual of Thevenin's (duals are discussed in Chapter 10). The theorem may
be stated as follows: any linear network containing an element connected to
two terminals A and B may be represented by an equivalent circuit between the
terminals of a current source Isc in parallel with a resistor R. The current Isc is
that which would flow through a short circuit connected between the terminals
A and B, and R is the equivalent resistance between them with the element
removed, with any voltage source replaced by a short circuit and with any
current source replaced by an open circuit.

Example 3.7

Calculate the maximum and minimum values of the potential difference across

the resistor r in the circuit of Fig. 3.22 if r is variable between 10 1~ and 100 1~.

Figure 3.22

R3 = 10s

Solution

First we put terminals A and B around the resistor r and represent the circuit by

its Norton equivalent as shown in Fig. 3.23, from which we see that

IL- [Rsc/(Rsc + r)]Isc (3.a2)