Massachusetts Institute of Technology

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Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.002

– Circuits & Electronics Fall 2007 Homework #2 Handout S07-015

Exercise 2.1: Determine the resistance of each network shown below as viewed from its port.

R

1

R

1

R

2

R

2

R

3 Network (A)

R

2

R

3

R

1

R

3 Network (C)

R

1

R

2

R

3 Network (B) Network (D) Exercise 2.2: For both networks shown below, find the voltage across each resistor. ( Hint: make use of the results of Exercise 2.1.

)

V

+ -

R

1

R

2

Network (A)

R

3

I R

2

R

1

Network (B)

R

3

Exercise 2.3: Following the node method, develop a set of simultaneous equations for the network shown at the top of the following page that can be used to solve for the three unknown node voltages. Express these equations in the form ⎡ e 1 ⎤ G ⎢ ⎣ e 2 ⎥ ⎦ = e 3 S, where G is a 3x3 matrix of conductance terms and S is a 3x vector of terms involving the sources. You need not solve the set of equations for the node voltages. 1 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

R

2

R

1

e

2

e

1

R

5

R

4

e

3

R

3

R

6

I

Exercise 2.4: Determine the power consumed by the 5Ω resistor in the network shown below. ( Hint: use the series/parallel simplification method shown in Section 2.4 of the course notes.

) 4 Ω 5 Ω 10V + 15 Ω 5 Ω Problem 2.1: Find the Thevenin and Norton equivalents of the following networks, and graph their i − v relations as viewed from their ports. ( Hint: use superposition for Network B.

)

i

+ v R

1

R

2

+

i

R v R

1

I -

Network (B) 2 Network (A) Problem 2.2: Problem 3.9 from Chapter 3 of A&L (page 87). 2 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

Problem 2.3: relations, and connected together through a single resistor, as shown below.

(B) Find the voltages v 1 and v 2 that result from the interconnection of N and N2.

i 1 R i 2 N 1 + v 1 − + v 2 − N 2 1 v 1 I 1 − V 1 (a) Network 1 (N1) i 1 v V 2 − I 2 2 (b) Network 2 (N2) i 2 i − v 3 Cite as: Anant Agarwal and Jeffrey Lang, course materials for 6.002 Circuits and Electronics, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu/), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].

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