Mit Electrical Electronics Open Ware 6.002-3 Handout S07015 Homework Hw2 565u58

Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.002 – Circuits & Electronics

Fall 2007

Homework #2

Handout S07-015

Helpful readings for this homework: Chapter 3. 1 3.3, 3.5-3.6.

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

R1

R2

R1 R2

R1

R3

R2

R3 Network (A)

R1

R2

R3

R3 Network (B)

Network (C)

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 + -

R1 R2

I

R3

R2 R1

Network (A)

R3

Network (B)

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

⎡

⎤

e1 ⎢ ⎥ G ⎣ e2 ⎦ = S, e3

( 1)

where G is a 3x3 matrix of conductance and S is a 3x 1 vector of 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. ed on [DD Month YYYY].

e1 R2

V +-

R5

R1 e 2

R4 e 3

R3

R6

I

Exercise 2.4: Determine the power consumed by the 15Ω resistor in the network shown below. (Hint: use the series/parallel simplification method shown in Section 2.4 of the course notes.)

5Ω

4Ω

10V +

5Ω

15Ω

-

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

R2 +

+ v

R2

i

R1

V +-

v R1

-

I

V +-

Network (B)

Network (A)

Problem 2.2: Problem 3.9 from Chapter 3 of A&L (page 1 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. ed on [DD Month YYYY].

Problem 2.3: Two networks, N 1 and N2, are described graphically in of their i−v

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

(A) Find the Thevenin and Norton equivalents of N1 and N2.

(B) Find the voltages v1 and v2 that result from the interconnection of N1 and N2.

R

i1

N1

+ v1 −

i2 + v2 −

N2

1

v1

v2 V2 I1 i1

−I2

i2

−V1

(b) Network 2 (N2)

(a) Network 1 (N1)

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. ed on [DD Month YYYY].