Capacitors
A capacitor is a passive element designed to store energy in its electric eld. Besides resistors, capacitors
are the most common electrical components. Capacitors are used extensively in el
V0(S)
Vi“) -
For the circuit shown in the ﬁgure, ﬁnd H (s) =
352 0.2F
1 1 5
0.2F a — =— =—
thJC s(0.2) s
1 10
0.1F—> =—
s(0.1) s
The circuit becomes that shown below.
Let Z =—|\
S
10 5 10
Calculate the voltage at nodes 1 and 2 in the circuit of the ﬁgure below using nodal analysis.
_,r'—'1 f2
“IT-TIE"
60 2:30:91
1
Atnode 1,
0—V1 0—V1 VZ—VJ 0
. + +_— = 60430
72 10 14
*(1+j2.5)
Determine V0 and I 0 in the op amp circuit of ﬁgure. Round to two decimal places.
Let the voltage between the *j4kQ capacitor and the IOkQ resistor be V1.
zzsmt—Vl V1-V0 V1-V0
_+— (1)
jjék 10k 20k
2
Use mesh analysis to determine current I 0 in the circuit shown below.
80 Q 0 j50 s2 70 Q
,r-_ _.h. .-. .-'- —- -"_5i_':_i€_" In, .-. .1. Ir-
9 _ -j30 s2 _ -j2 Q
20 /’-160° V EDI/410° V
Consider t
Use mesh analysis to determine current I 0 in the circuit shown below.
60 Q '5' le Q 90 Q
,r-_ _.h. I.-._ .-'- -"_5i_':_i€_" In, _.-.I .-'\._ Ir-
fir-.‘Tv-IFT-r-i-If
_ -j70 s2 _ -j2 Q
10 /40° V
Using the superposition principle, find i [5 cos(2t — 58°) V], i[3 cos(2t + 14°) A], ix in the
circuit shown below, wherei[5 cos(2t — 58°) V] is due to the voltage source and
i[3 cos(2t + 14°) A] is d
Using mesh analysis, obtain I 0 in the circuit shown in ﬁgure. Round your intermediate
calculations and ﬁnal answers to two decimal places if necessary.
12490“ V
Consider the circuit below.
Clearl
Use nodal analysis to ﬁnd the current v 0 , i0 in the ﬁgure. Let i s = 6 cos(5001 + 15°) A.
Round your answers to three decimal places.
100mH
co = 500
lOOmH ijL =j500 x 0.1 =j50
1 1
10 or a _— =
Using an origin at to = 1, H dB = 0, construct the Bode amplitude plot for
5 x 108 s(s + 100)
H(s) =—.
(s + 20)(s + 1,000)3
Reorganizing H(s) gives
H(S )
(20)(1,000)3 (LHX 5 +1)3
U]
0:
/"'"'-\
,_.
C
Previously we considered circuits with a single storage element (a capacitor or an inductor). Such circuits
are rst-order because the differential equations describing them are rst-order. Now we will
Capacitors
A capacitor is a passive element designed to store energy in its electric eld. Besides resistors, capacitors
are the most common electrical components. Capacitors are used extensively in el
Nortons Theorem
In 1926, about 43 years after Thevenin published his theorem, E. L. Norton,
an American engineer at Bell Telephone Laboratories, proposed a similar
theorem.
Nortons theorem states that
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Open a chrome browser (or your
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and navigate to everycircuit.com.
Create a new account for your group
by choosing sign in. Note
Apply Mesh Analysis to find i1 and i in the circuit below:
MESH ANALYSIS WITH CURRENT SOURCES
Applying mesh analysis to circuits containing current sources (dependent or independent) may appear
compli
ProfessorMason
Engineering44
http:/www.youtube.com/watch?v=ycHwPwjI0lM&feature=player_embedded
The circuit photographed below includes three identical light bulbs and two identical batteries,
wired as
We will attach a hotdog to a line cord and apply a 120 V potential across it.
result:
A: Nothing will happen
B: The hotdog will quickly crisp and then burn
C: The hotdog will slowly cook
D: The hotdog
The circuit photographed below includes two identical light bulbs and three identical
batteries, wired as seen in the photograph. In this photograph the switch is OFF, that is,
the circuit is open at
Find the Thevenin and Norton equivalent circuits at terminals a -b for each of the circuits in
the ﬁgure.
1'40 52 20 9
TL? 1‘ ﬁﬁﬁ‘ﬁ—D n
4050" V + 130 9
1: b
To ﬁnd Z Th, consider the circuit in the
Obtain V 0 in the ﬁgure below using nodal analysis. Give your ﬁnal answers rounded to two
decimal places.
0.6 VD
We have a supernodc as shown in the circuit below.
1'29
Notice that V0 = V].
At the
Solve for £1 , i 2 , i 0 in ﬁgure using mesh analysis. Round your answers to two decimal places.
“HEW”?-
10 cos(2t) V [\‘i' . 8 sin(2t) V
(1) =2
10 eos(2t) —> 10 4 0°
8 sin(2t) —> 8 4 790° =ij8
3
Source Modeling
Source modeling provides an example of the usefulness of the Thevenin or the Norton equivalent. An
active source such as a battery is often characterized by its Thevenin or Norton
equi
Nortons Theorem
In 1926, about 43 years after Thevenin published his theorem, E. L. Norton,
an American engineer at Bell Telephone Laboratories, proposed a similar
theorem.
Nortons theorem states that
Engineering Dictionary:
Barium: What to do with someone when they die
Tablet: A little table
Node: I knew it but now I dont.
MESH ANALYSIS
Mesh analysis is another general procedure for analyzing circ