Problems
Perspective (Preceding Chapter 2)
2.1
The circuit of Fig. P2.1 has a nonlinear device
for which
i
=
√
v
. Determine
v
by graphical analysis.
+
+
12
6
3
2
+
v
i
Figure P2.1
2.2
Repeat Problem 2.1, but let
i
= 2
√
v
and reduce
the 2A source to 1 A.
2.3
The circuit of Fig. P2.3 has a nonlinear device
for which
i
= 2
v
3
/
2
(with
i
in mA). Determine
v
by
graphical analysis.
x
+
+
+
12
v
(mA)
+
v
i
x
v
1 k
Ω
2 k
Ω
2
Figure P2.3
2.4
Repeat Problem 2.3 but let
v
x
appear across the
2kΩ resistor (with positive node to the left).
2.5
A 10V source with Thevenin resistance
R
t
con
nects to a nonlinear device for which
i
= 2(
v

1)
2
(with
i
in mA) subject to
v
≥
1 V. The device has
zero current otherwise. Use a graphical procedure to
determine
R
t
such that
i
= 4 mA.
2.6
A current source
I
n
with 1kΩ Norton resistance
connects to a nonlinear device for which
i
=
√
v

2
(with
i
in mA) subject to
v
≥
2 V. The device has
zero current otherwise. Use a graphical procedure to
determine
I
n
such that
i
= 8 mA.
2.7
The circuit of Fig. P2.7 has a nonlinear resistor
for which
v
=
ikR
i
≥
0
iR/k
i <
0
.
In this expression,
k
is a dimensionless constant that
is subject to 0
≤
k
≤
1. The oldfashioned electro
mechanical ammeter measures timeaveraged current
< i >
=
1
T
Z
t
0
i
(
t
)
dt ,
where
T
= 2
π/ω
is the period of the ac signal.
(a) Determine
< i >
when
k
= 1 (the limiting case
for a linear resistor).
(b) Determine
< i >
when
k
= 0 (the limiting case
for an ideal diode).
(c) Use graphical analysis to explain qualitatively
the variation in
< i >
as
k
is varied between 0
and 1 (the “diode” becomes less and less ideal).
(d) Determine
k
such that
< i >
= ˜
v/
10
R
.
Note: The disparity of the results for parts a
and b
reflects diode function as a
detector
of ac amplitude.
This is an important application (particularly for the
early days of radio).
+
+
v
i
R
v sin
ω
t
∼
ammeter
k
Figure P2.7
c
2010
Edward W. Maby
All Rights Reserved
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Section 2.1
2.8
In the study of chemistry, one learns that the
number of molecules in one mole of any substance is
given by Avagadro’s number (6
.
02
×
10
23
).
(a) Look up the density of gold. Then estimate the
free electron concentration in gold, assuming one
free electron per atom.
(b) The conductivity of gold is 4
.
1
×
10
5
(Ωcm)

1
.
Estimate the electron mobility in gold.
2.9
The resistivity of copper is 1
.
7
×
10

6
Ωcm.
Determine the resistance of 100 feet of AWG #22
copper wire with 0.645mm diameter.
2.10
In the design of a particular integrated circuit,
the aluminum interconnect lines are constrained to
have 1
μ
m thickness. Any line is subject to certain
failure (by becoming an open circuit) if it regularly
carries a current density that exceeds 5
×
10
5
A / cm
2
.
Careful simulations indicate that currents as high as
15 mA can be expected throughout the circuit.
(a) Determine the minimum acceptable line width.
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 Puvvada
 Fig, Edward W. Maby

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