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The following problem serves to give you a better qualitative idea as to
how the circuit outputs vary as different values are chosen for the resistor R.

In-Class Exercise
Pb. 3.7 This problem still refers to the circuit of Figure 3.1.
a. Redraw the lines L and L , using the previous values for the circuit
1
2
parameters.
b. Holding the graph for the case R = 100Ω, sketch L and L again
2
1
for R = 50Ω and R = 500Ω. How do the values of the voltage and
the current change as R increases; and decreases?
c. Determine the largest values of the current and voltage that can
exist in this circuit when R varies over non-negative values.
d. The usual nomenclature for the circuit conditions is as follows: the
circuit is called an open circuit when R = ∞, while it is called a
short circuit when R = 0. What are the (V, I) solutions for these two
cases? Can you generalize your statement?

Now, to validate the qualitative results obtained in Pb. 3.7, let us solve
analytically the L and L system. Solving this system of two linear equations
1 2
in two unknowns gives, for the current and the voltage, the following
expressions:

 R 
VR() =   RR+ 1   V s (3.6)

 1 
IR() =   RR+ 1   V s (3.7)

Note that the above analytic expressions for V and I are neither linear nor
affine functions in the value of the resistance.

In-Class Exercise

Pb. 3.8 This problem still refers to the circuit of Figure 3.1.
a. Keeping the values of V and R fixed, sketch the functions V(R)
1
s
and I(R) for this circuit, and verify that the solutions you found
previously in Pbs. 3.7 and 3.8, for the various values of R, agree
with those found here.

© 2001 by CRC Press LLC