TAILIEUCHUNG - Electric Circuits, 9th Edition P16

Electric Circuits, 9th Edition P16. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 126 Techniques of Circuit Analysis dv2 3 4 3 4 g2 2 3 4 dR A2 3 4 7 3 4 2 Figure Circuit used to introduce sensitivity analysis. We now consider an example with actual component values to illustrate the use of Eqs. and . EXAMPLE Assume the nominal values of the components in the circuit in Fig. are R 25 ft R2 5 ft R3 50 ft R4 75 ft Ig 12 A and Ig2 16 A. Use sensitivity analysis to predict the values of and v2 if the value of R is different by 10 from its nominal value. Solution From Eqs. and we find the nominal values of 1 and v2. Thus 25 3750 16 - 5 125 3750 12 30 125 3750 25 V 4-99 and 3750 30 16 25 12 1 30 i25jV375T - 7 9 V 4-W0 Now from Eqs. and we can find the sensitivity of V and v2 to changes in . Hence dv 3750 5 125 - 3750 16 - 3750 5 125 12 K 30 125 3750 2 7 V ft and dv2 _ 3750 3750 16 - 5 125 3750 12 dRi 7500 2 V ft. Practical Perspective 127 How do we use the results given by Eqs. and Assume that 7 is 10 less than its nominal value that is Ry il. Then il and Eq. predicts Vy will be A-yj V. Therefore if Ry is 10 Less than its nominal value our analysis predicts that Vy will be Vy 25 - V. Similarly for Eq. we have Au2 V v2 90 - V. We attempt to confirm the results in Eqs. and by substituting the value Ry fl into Eqs. and . When we do the results are V v2 V. Why is there a difference between the values predicted from the sensitivity analysis and the exact values computed by substituting for R in the equations for Vy and v2 We can see from Eqs. and that the sensitivity of Vt and v2 with respect to Ry is a function of Ry because Ry appears in the denominator of both Eqs. and . This means that as changes the sensitivities change and hence we cannot expect Eqs. and to give exact results for Large changes in Ry. Note that .

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