Explanation Given data: Refer to Figure given in the textbook. The current source is I g 1 = 12 A and I g 2 = 16 A . The resistors R 1 = 25 Ω , R 2 = 5 Ω , R 3 = 50 Ω , and R 4 = 75 Ω . Calculation: Refer to the equation given in the textbook, the sensitivity of the node voltage v 1 for the given circuit is as follows, v 1 = R 1 { R 3 R 4 I g 2 − [ R 2 ( R 3 + R 4 ) + R 3 R 4 ] I g 1 } ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 (1) The sensitivity of v 1 with respect to I g 1 is calculated by differentiating equation (1) with respect to I g 1 as follows, d v 1 d I g 1 = R 1 { R 3 R 4 ( 0 ) − [ R 2 ( R 3 + R 4 ) + R 3 R 4 ] ( 1 ) } ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 { ∵ I g 2 = 0 , I g 1 = 1 } = R 1 { 0 − [ R 2 ( R 3 + R 4 ) + R 3 R 4 ] } ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 d v 1 d I g 1 = − R 1 [ R 2 ( R 3 + R 4 ) + R 3 R 4 ] ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 (2) From equation (4.46) in the textbook, the sensitivity of the node voltage v 2 for the given circuit is as follows, v 2 = R 3 R 4 [ ( R 1 + R 2 ) I g 2 − R 1 I g 1 ] ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 (3) The sensitivity of v 2 with respect to I g 1 is calculated by differentiating equation (2) with respect to I g 1 as follows, d v 2 d I g 1 = R 3 R 4 [ ( R 1 + R 2 ) ( 0 ) − R 1 ( 1 ) ] ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 { ∵ I g 2 = 0 , I g 1 = 1 } = R 3 R 4 [ 0 − R 1 ] ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 d v 2 d I g 1 = − R 1 R 3 R 4 ( R 1 + R 2 ) ( R 3 + R 4 ) + R 3 R 4 (4) Substitute 25 for R 1 , 5 for R 2 , 50 for R 3 , and 75 for R 4 in equation (2) to find the sensitivity of v 1 with respect to I g 1

11th Edition

ISBN: 9780134746968

Author: James W. Nilsson, Susan Riedel

Publisher: PEARSON

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Chapter 4, Problem 105P

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Find the values of node voltage v1 and v2 if Ig1 is reduced to 11 A of the given circuit using PSPICE.

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Chapter 4, Problem 104P

Chapter 4, Problem 106P

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Find the values of node voltage v1 and v2 if Ig1 is reduced to 11 A of the given circuit using PSPICE.

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