EE 101
Handout # 3
Professor Abbas El Gamal
Jan. 22, 2002
Homework #1 Solutions
1.
(a) Let
v
denote the output voltage of the CD player. The voltage limit is

v
 ≤
5.
The current into the receiver is
v/R
, so the current limit is

v/R
 ≤
0
.
01, or
equivalently,

v
 ≤
0
.
01
R
. Therefore for 0
.
01
R <
5,
i.e.
,
R <
500Ω, the current
limit is more stringent than the voltage limit. For
R
≥
500Ω, the voltage limit is
more stringent.
(b) When
R
= 10kΩ (a typical value), the CD player output is limited to
±
5V by
the voltage limit; the current limit is irrelevant. The maximum power in this case
occurs for
v
= 5V (or
v
=

5V); it is
p
max
= 5
2
/
10kΩ = 2
.
5mW. For
R
= 400Ω,
on the other hand, the CD player output would be limited to
±
4V by the current
limit.
Another way of looking at this is to sketch the given limits on a
v
–
i
plot. This
forms a box in the plane. Note that the set of points inside the box represents all
the possible voltagecurrent combinations the amplifier can handle. This sketch
looks like:
i
v
10mA

10mA
5V

5V
R
≤
500Ω
R
= 500Ω
R
≥
500Ω
Connecting a resistor across the terminals of the amplifier can be represented by
sketching
v
=
iR
on the same plot.
This equation gives a straight line whose
1
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slope is 1
/R
. Thus a line along the vertical axis corresponds to infinite slope or
zero resistance, and a line along the horizontal axis corresponds to zero slope or
infinite resistance. In other words, these two examples are a short circuit and an
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 Fall '08
 PingLi
 Volt, Resistor, iL, Electrical resistance, Professor Abbas El Gamal

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