# Homework Given January
16, 2007

## Due January23, 2007

These aren't homework problems per se; the Exercises are
intended as a study aid for those reading the chapter. These are selected to make sure that the
intended points stick with the student.

## Live Links to the Exercises

Exercise 1.1

Exercise 1.5

Exercise 1.12

## Exercise 1.1

Plot the voltage-current curve of resistors of 1 k, 5 k, and 20 k,

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## Exercise 1.5

Find the value of in Figure 1.5 if

It's tempting to use a Norton equivalent of , , and , because that would result in two current sources in
parallel across two resistors in parallel, a very simple circuit to solve. However, the section is on superposition, so
we will solve it by superposition.

The component of from is

and the component from is identical,

.

The component of from is

.

The final value of is the sum of the
components from , , and ,

.

For the values given in the problem statement, is

.

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## Exercise 1.12

Plot the v-I equation of the circuit of Figure 1.11 if the
value of is changed to

.

The figure is part of Example 1.3, which is a superposition
example. To follow the intent of the
exercise, we will solve it by superposition.

Note that the zig-zag transistor
model geometry of Figure 1.11 has been changed here to the more familiar ladder
configuration that we use for circuit analysis.
To plot the *v-I* characteristic
of and , we need to find the open circuit voltage and short circuit
current. In class, I solved this circuit
directly instead of using superposition as in Example 1.3, which is the context
for the figure. Here, we use
superposition.

The component of the open circuit voltage due to is found by finding and noting that the
controlled current source and form a Norton
equivalent across the terminals which is measured. This we have

The short circuit current is simply the controlled current
source current, negated because is positive out the
terminal, opposite the direction of the arrow in the controlled current source,

.

The voltage source drives current through
opposite than that of but its effect on the
controlled current source is otherwise identical, so we have

By superposition, the open circuit voltage is the sum of the
two voltages due to and , and the short circuit current is the sum of the currents
due to and ,

For the values given in the problem,

and, finally, the total open circuit voltage and short
circuit current are

We plot the *v-i* curve from the open circuit voltage, when current is
zero, and the short circuit current, when the voltage is zero, as a straight
line between these points as below.

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