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Figure 333 Computation of Th venin resistance e
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Figure 334 Equivalent resistance seen by the load
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Figure 335 An alternative method of determining the Th venin resistance e
Summarizing the procedure, we can produce a set of simple rules as an aid in the computation of the Th venin (or Norton) equivalent resistance for a linear e resistive circuit:
F O C U S O N M E T H O D O L O G Y
Computation of Equivalent Resistance of a One-Port Network 1 Remove the load 2 Zero all independent voltage and current sources 3 Compute the total resistance between load terminals, with the load removed This resistance is equivalent to that which would be encountered by a current source connected to the circuit in place of the load We note immediately that this procedure yields a result that is independent of the load This is a very desirable feature, since once the equivalent resistance has been identi ed for a source circuit, the equivalent circuit remains unchanged if we connect a different load The following examples further illustrate the procedure
EXAMPLE 311 Thevenin Equivalent Resistance
Problem
Find the Th venin equivalent resistance seen by the load RL in the circuit of Figure 336 e
Solution
Known Quantities: Resistor and current source values
Part I
Circuits
Find: Th venin equivalent resistance RT e
R3 = 10 ; R4 = 20 ; R5 = 10
Schematics, Diagrams, Circuits, and Given Data: R1 = 20
; R2 = 20 ; I = 5 A;
Assumptions: Assume reference node is at the bottom of the circuit Analysis: Following the methodology box introduced in the present section, we rst set the current source equal to zero, by replacing it with an open circuit The resulting circuit is depicted in Figure 337 Looking into terminal a-b we recognize that, starting from the left (away from the load) and moving to the right (toward the load) the equivalent resistance is given by the expression
R1 R2
RT = [((R1 ||R2 ) + R3 ) ||R4 ] + R5 = [((20||20) + 10) ||20] + 10 = 20
Figure 337 Comments: Note that the reduction of the circuit started at the farthest point away from
the load
EXAMPLE 312 Thevenin Equivalent Resistance
Problem
Compute the Th venin equivalent resistance seen by the load in the circuit of Figure 338 e
V + _
Solution
Known Quantities: Resistor values Find: Th venin equivalent resistance RT e
3
Resistive Network Analysis
R3 = 1 ; I = 1 A, R4 = 2
Schematics, Diagrams, Circuits, and Given Data: V = 5 V; R1 = 2 Assumptions: Assume reference node is at the bottom of the circuit
; R2 = 2 ;
Analysis: Following the Th venin equivalent resistance methodology box, we rst set e the current source equal to zero, by replacing it with an open circuit, then set the voltage source equal to zero by replacing it with a short circuit The resulting circuit is depicted in Figure 339 Looking into terminal a-b we recognize that, starting from the left (away from the load) and moving to the right (toward the load), the equivalent resistance is given by the expression
RT = ((R1 ||R2 ) + R3 ) ||R4
= ((2||2) + 1) ||2 = 1
Comments: Note that the reduction of the circuit started at the farthest point away from
the load
As a nal note, it should be remarked that the Th venin and Norton equivalent e resistances are one and the same quantity: RT = RN (329)
Therefore, the preceding discussion holds whether we wish to compute a Norton or a Th venin equivalent circuit From here on we shall use the notation RT e exclusively, for both Th venin and Norton equivalents Check Your Understanding e Exercise 313 will give you an opportunity to explain why the two equivalent resistances are one and the same
Check Your Understanding
313 Apply the methods described in this section to show that RT = RN in the circuits of Figure 340
RT 3 k 2 k 5 k 5 k 5V + _ b RL 25 k a
VT + _
RL IN
Figure 340 Figure 341
314 Find the Th venin equivalent resistance of the circuit of Figure 341 seen by the e load resistor, RL 315 Find the Th venin equivalent resistance seen by the load resistor, RL , in the circuit e of Figure 342 316 For the circuit of Figure 343, nd the Th venin equivalent resistance seen by the e load resistor, RL
Part I
2 6 10 V + _ 05 A 4 10 b 3 RL 2 5
Circuits
3 k 20 V + _ 6 k 2 k a
1 M
2 k
6 k
3 k
317 For the circuit of Figure 344, nd the Th venin equivalent resistance seen by the e load resistor, RL
10 1 10 12 V + _ b 20 RL a
Computing the Thevenin Voltage This section describes the computation of the Th venin equivalent voltage, vT , for e an arbitrary linear resistive circuit The Th venin equivalent voltage is de ned as e follows:
+ One-port network v OC
The equivalent (Th venin) source voltage is equal to the open-circuit e voltage present at the load terminals (with the load removed)
+ v OC = vT
This states that in order to compute vT , it is suf cient to remove the load and to compute the open-circuit voltage at the one-port terminals Figure 345 illustrates that the open-circuit voltage, vOC , and the Th venin voltage, vT , must e
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