barcode reader code in asp.net va V va +I =0 R1 R2 Substituting numerical values, we nd that va = vOC = vT = 27 V in Software

Print QR Code 2d barcode in Software va V va +I =0 R1 R2 Substituting numerical values, we nd that va = vOC = vT = 27 V

va V va +I =0 R1 R2 Substituting numerical values, we nd that va = vOC = vT = 27 V
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va R1 I V + _ R2 + vOC vb 3 i 27 V + _ 6
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Figure 354 Th venin e equivalent
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Finally, we assemble the Th venin equivalent circuit, shown in Figure 354, and e reconnect the load resistor Now the load current can be easily computed to be: i= 27 vT =3A = RT + R L 3+6
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Comments: It may appear that the calculation of load current by the Th venin equivalent e method leads to more complex calculations than, say, node voltage analysis (you might wish to try solving the same circuit by nodal analysis to verify this) However, there is one major advantage to equivalent circuit analysis: Should the load change (as is often the case in many practical engineering situations), the equivalent circuit calculations still hold, and only the (trivial) last step in the above example needs to be repeated Thus, knowing the Th venin equivalent of a particular circuit can be very useful whenever we e need to perform computations pertaining to any load quantity
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318 With reference to Figure 346, nd the load current, iL , by mesh analysis, if vS = 10 V, R1 = R3 = 50 , R2 = 100 , RL = 150
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319 Find the Th venin equivalent circuit seen by the load resistor, RL , for the circuit e of Figure 355 320 Find the Th venin equivalent circuit for the circuit of Figure 356 e
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a 100 50 V + _ 40 1 A 2 1 A 4 20 20 10 b 24 a
05 A 60
+ 15 V 025 A _
10 RL 30 b
Computing the Norton Current The computation of the Norton equivalent current is very similar in concept to that of the Th venin voltage The following de nition will serve as a starting point: e
De nition The Norton equivalent current is equal to the short-circuit current that would ow were the load replaced by a short circuit
An explanation for the de nition of the Norton current is easily found by considering, again, an arbitrary one-port network, as shown in Figure 357, where the one-port network is shown together with its Norton equivalent circuit It should be clear that the current, iSC , owing through the short circuit replacing the load is exactly the Norton current, iN , since all of the source current in the circuit of Figure 357 must ow through the short circuit Consider the circuit of Figure 358, shown with a short circuit in place of the load resistance Any of the techniques presented in this chapter could be employed to determine the current iSC In this particular case, mesh analysis is a convenient tool, once it is recognized that the short-circuit current is a mesh current Let i1 and i2 = iSC be the mesh currents in the circuit of Figure 358 Then, the following mesh equations can be derived and solved for the short-circuit current: (R1 + R2 )i1 R2 iSC = vS R2 i1 + (R2 + R3 )iSC = 0 An alternative formulation would employ nodal analysis to derive the equation vS v v v = + R1 R2 R3 leading to v = vS R2 R3 R1 R3 + R 2 R3 + R 1 R2
One-port network
RT = RN
Figure 357 Illustration of Norton equivalent circuit
Short circuit replacing the load v R3
vS + _
i SC
Figure 358 Computation of Norton current
3
Resistive Network Analysis
Recognizing that iSC = v/R3 , we can determine the Norton current to be: iN = v v S R2 = R3 R1 R3 + R 2 R3 + R 1 R2
Thus, conceptually, the computation of the Norton current simply requires identifying the appropriate short-circuit current The following example further illustrates this idea
F O C U S O N M E T H O D O L O G Y
Computing the Norton Current 1 2 3 4 Replace the load with a short circuit De ne the short circuit current, iSC , to be the Norton equivalent current Apply any preferred method (eg, nodal analysis) to solve for iSC The Norton current is iN = iSC
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