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# Consider the circuit shown in Figure 7.1.2. Let I1, I2, and I3 be the currents through ISBN: 9781119256007 392

## Solution for problem 16 Chapter 7.1

Elementary Differential Equations and Boundary Value Problems | 11th Edition

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Problem 16

Consider the circuit shown in Figure 7.1.2. Let I1, I2, and I3 be the currents through the capacitor, resistor, and inductor, respectively. Likewise, let V1, V2, and V3 be the corresponding voltage drops. The arrows denote the arbitrarily chosen directions in which currents and voltage drops will be taken to be positive. a. Applying Kirchhoffs second law to the upper loop in the circuit, show that V1 V2 = 0. (15) In a similar way, show that V2 V3 = 0. (16) b. Applying Kirchhoffs first law to either node in the circuit, show that I1 + I2 + I3 = 0. (17) c. Use the current-voltage relation through each element in the circuit to obtain the equations CV_ 1 = I1, V2 = RI2, L I_ 3 = V3. (18) d. Eliminate V2, V3, I1, and I2 among equations (15) through (18) to obtain CV_ 1 = I3 V1 R , L I_ 3 = V1. (19) Observe that if we omit the subscripts in equations (19), then we have the system (2) of this section. 1

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Section 1.5 Reduced Echelon Form 10 r If we get   then the solution is 01 s x1= r and x =2s.  0 r  0 s If we get 001 t then the solution is   x1= r, x2= s and x =3t. With many systems, particularly rectangular systems, this isn't possible. We need a form to show us when the augmented matrix is "as reduced as possible"....

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##### ISBN: 9781119256007

The full step-by-step solution to problem: 16 from chapter: 7.1 was answered by , our top Math solution expert on 03/13/18, 08:17PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 75 chapters, and 1655 solutions. The answer to “Consider the circuit shown in Figure 7.1.2. Let I1, I2, and I3 be the currents through the capacitor, resistor, and inductor, respectively. Likewise, let V1, V2, and V3 be the corresponding voltage drops. The arrows denote the arbitrarily chosen directions in which currents and voltage drops will be taken to be positive. a. Applying Kirchhoffs second law to the upper loop in the circuit, show that V1 V2 = 0. (15) In a similar way, show that V2 V3 = 0. (16) b. Applying Kirchhoffs first law to either node in the circuit, show that I1 + I2 + I3 = 0. (17) c. Use the current-voltage relation through each element in the circuit to obtain the equations CV_ 1 = I1, V2 = RI2, L I_ 3 = V3. (18) d. Eliminate V2, V3, I1, and I2 among equations (15) through (18) to obtain CV_ 1 = I3 V1 R , L I_ 3 = V1. (19) Observe that if we omit the subscripts in equations (19), then we have the system (2) of this section. 1” is broken down into a number of easy to follow steps, and 178 words. Elementary Differential Equations and Boundary Value Problems was written by and is associated to the ISBN: 9781119256007. This textbook survival guide was created for the textbook: Elementary Differential Equations and Boundary Value Problems, edition: 11. Since the solution to 16 from 7.1 chapter was answered, more than 243 students have viewed the full step-by-step answer.

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