4
Powerful Circuit Theorems
4.1 For the circuit below find Req .
(1) 5 ⌦
O
(2) -10 ⌦
É
test
Ies
A
Itest 1 21
B
3
Itest I
vtest lo
I
Rea
(3) 3 ⌦
(4) 12 ⌦
(5) 4 ⌦
(6) -12 ⌦
(7) 0 ⌦
(8) None of the above.
4.2 For the following linear circuit, complete the table below.
Vo Ns
2 5
BIS
Be
Vo 5 6 2 1 4V
(1) 4 V
(2) 3 V
(3) 2 V
(4) 5 V
(5) -4 V
(6) 0 V
(7) -3 V
(8) None of the above.
42
ion
4.3 What is the correct source transformation of the portion inside the box
keeping every element outside the box unchanged?
RailRs
I
0
I
43
Iz I
RallRz
RdRD
4.4 Which of the circuits, shown as (1) to (7), is equivalent to the following?
Tito
ÉIIÉÉ
or
Yet
Egor
I
b
Toy
4.5 Suppose that you take the following measurement on the 2-terminal linear
circuit in the box below:
when RL = 1, you measure VL = 32V
when RL = 4⌦, you measure VL = 8V
now, if RL = 1, find the value of VL .
Har
I
9
O
Ig Recs K 32V
Ri
ar
VE SV
Re Req 12V
44
Vtu 3 V
Req 121
VL É Vth IOU
4.6 What is the Norton equivalent representation of the linear circuit?
Voc GV
Isa 2A
or
Vth GV
Req EA
ME
4.7 What is the value of the voltage V0 when V1 = 3V and I1 = 1A? Assume
that there are no independent sources within the linear circuit box.
Vo AV BI
23 B 5
Vo 3.3 111.5 4
45
31
tatty
4.8 Initial values for the voltage (V1 ) and current (I2 sources in the circuit
shown produce an output potential, V0 , equal to 16V. V0 is a linear function of V1 and I2 according to the equation,
I
V0 = AV1 + BI2 .
If doubling I2 changes V0 to 20V when V1 remains constant, find V1 (in
V).
AV BIZ 16
Av 21312 20
AV 12
petition
ion
IV
4.9 The linear resistive circuit below contains only resistors and dependent
sources. Measurements of V0 for different input excitations are tabulated
below. Find V0 when I1 = 0.2A and V2 = 2V (in V).
Vo a I BV
O
2 80
B 0.5
vo so o
0.5 121 15
46
4.10 Find the equivalent resistance of the following circuit:
O
I
vtest
I
0
Itest
Itest Vx 2Vx
Itest Vx Vtest
Reg i r
4.11 For the circuit below find the Thevenin equivalent resistance with respect
to nodes A and B.
F Ix
IxR
(1) R/2
O
(2) 2R
(3) R/3
(4) 3R
(5) R/4
(6) 4R
(7) R
(8) None of the above.
47
4.12 The linear circuit below consists of resistors and sources only. Experiments
were performed to evaluate circuit parameters. Two current/voltage relationships were found to be:
v = 10V, iL = 0A
v=
10V, iL = 2A
Find the value of the Thevenin equivalent resistance, RTh , for the linear
circuit (in ⌦).
Uh
Rea
o
til
I
U IOU in OA
V lov
E
Vth IOU
IL2A
Utotal ZOU Reg
VII Ion
4.13 Assume that a linear circuit is excited by two voltage sources: v1 (t) and
v2 (t). The circuit is used to power a load resistor R. When only vs (v2 ) is
a
active, the average power consumed on the resistor is P1 (P2 ). What is the
average power consumed on the resistor R when both sources are active?
(1) P1 + P2
signal is missing
(2) P1
(3) P2
(4)
2
v1
v2
+ 2
R
R
(5) Cannot be determined with the given information
jper
4.14 For the circuit below find the current I0 .
A GA 3A
VAj
B 3A VEY VBg
Io
y
48
VB
0.5A
3.5
(1) 3 A
(2) -9 A
(3) -1 A
(4) 0.25 A
(5) 4 A
(6) 0.5 A
(7) 9 A
(8) None of the above.
4.15 Find the Norton current IN in the circuit below.
1 I OA
In IOA
(1) -10 A
(2) 12 A
(3) 0 A
O
(4) 10 A
(5) 5 A
(6) 0.1 A
(7) -0.1 A
(8) None of the above.
4.16 Find the value of Vth in the circuit below between the terminals ab.
Io 3A
Vth IOI ar GOV
O
(1) 60 V
(2) -60 V
(3) 0 V
(4) 20 V
(5) 40 V
(6) 30 V
(7) -30 V
(8) None of the above.
4.17 For the circuit below, find Req .
I Ai
Piz
49
vtest
42 212 221 4217 0
42 2 liz in Vtest O
VII
4
(1) 12.5 ⌦
(2) -8 ⌦
(3) 10 ⌦
(4) -4 ⌦
(5) -10 ⌦
(6) 20 ⌦
O
(7) 4 ⌦
(8) None of the above.
4.18 Find the Thevenin (open circuit) voltage Vth in the circuit below between
the terminals ab.
Io 4A
O
(1) 20 V
(2) -60 V
(3) 0 V
(4) 60 V
(5) 40 V
(6) 30 V
(7) -30 V
(8) None of the above.
4.19 For the circuit below, find the equivalent resistance (Req ) between terminals (a) and (b).
I
YEI TI
in
test
O
A
B
IAB I't II
IAB I Itest
I Itest
50
I 21
I 21
test
I
I
I
Zr IAB Ir
IAB 2Itest
4Itest
4.20 If we increase the current source (I) in the figure below from 2A to 4A,
find the change in the voltage V1 in unit of volt?
(Method: rV1 = V1(for I=4A) V1(for I=2A) )
B IAB It 3A
A
FAB
B
A IAB 3A I
I
I I
I
I 31
131
V II 4A
RV
V
V II
4.21 Find the Norton equivalent current (IN ) at the terminal AB.
X
IN
X
VR OV
0
I
Er 3A
51
2A GV
4.22 Find the value of Rload such that maximum power is delivered across the
load. Also, find the value of maximim power delivered to the load (Pmax )?
Gators
ait
o
Road Reg Zor
Pmax 121712.201 80W
4.23 In the following figure, using the superposition principle Vout = ↵Vs + Is .
Find the expressions of ↵ and .
TIKI
Us
Vout Us
rout
p
R
Etta's
Vout Is EYE
52
B EYE
4.24 Find the equivalent resistance Req across terminals AB.
A
l
Yo
B
O
VAB IOIx Ir
Reg VIE
4.25 The Req of the network shown below is: (in ⌦)
f Is
Vs
2 Is
Reg 2 r
53
ion
4.26 In the circuit shown below, VOUT can be written as a linear combination
of Vs and Is , i.e., VOUT = ↵Vs + Is . What are the correct values for ↵
and ?
ÉYÉY É
YÉ
a
sr
ft
151 515 I's
201 5 Is
Vout 101 2.5Is
s
6 25
4.27 Reduce the following circuit to its Thevenin equivalent.
it
104 513 1 7.511
1011 5 Itest Ii 7.51
I
7.511 5Itest
lvth ior.FI
vtest IOI
4.28 What must R1 be such that the equivalent resistance, Req , is 5⌦?
0
22
my
III.me
Itest 1.51
treat
YtRix
Vx
Red
Vx 2IxtRiIx
2 12
Rea
YI
54
0.5
4.29 Find the absolute value of the voltage across R1 .
VA
lov
1 1
O
O
5
71
VA O
o
4.30 What is the Thevenin equivalent representation of the circuit?
É
IT
in
4.31 The equivalent resistance of the following circuit is 5⌦. Calculate the value
of ↵.
Itest
Itai
test
55
IOI
Rea
VIII
2 1
(1) -3
(2) -2
(3) -1
(4) 0
O
(5) 1
(6) 2
(7) 3
(8) None of the above.
4.32 Find the VOC and RTh of the two-terminal linear network shown below.
EEN
It
In
We 0.5L
1.5 EIEEIIao
Voc 0.25A.at A.ir
ii iAlliz Altitialtziato
(1) VOC = 0V and RTh = 0⌦
(2) VOC = 1V and RTh = 0⌦
theft
(3) VOC = 1V and RTh = 1⌦
(4) VOC = 2V and RTh = 1⌦
(5) VOC = 1V and RTh = 2⌦
(6) VOC = 2V and RTh = 2⌦
(7) VOC = 2V and RTh = 3⌦
(8) VOC = 3V and RTh = 3⌦
(9) None of the above.
4.33 Using the source transformation or any other analysis technique, find the
value of the Norton Equivalent current source (in A) for the circuit below.
I
1
56
GA 44 34
In I't IA 4A
rear
ninny
E Iv
V 3AxzÉ rx2r
IV
4.34 Solve the problems below:
D
4.35 Solve the problems below:
a
Vx loux
a
o
o
DI Road Req Er
Pmax
VEI.VE
tOVT
3Vx
FEEL
six
Voct4
z sve
Voc
ion
KIF
77 21 43
34 2
Vx
É
0.51W
4.36 Solve below:
VA
VB
Yf 2 V81 O
V 2 0
KVA z
a 3
D FLAX
RAH
YI B
13A
f 2A x
57
I
VÉ
0.5A
0.5A
Vx YE x5r Ivtest
4.37 Find the indicated node voltage using (a) source transformation, (b) superposition.
Haakrijortgat
Ibl 12Vx 33 isux
24V x
4.38 A source that is represented by its Thevenin equivalent circuit is shown
in (a). Find the current that leaves the circuit (i.e. the current that flows
through node a) when the two circutis are attached.
I
I zor
ÉETI
ITGorME
or
Gov
tYftp.a
I
FETE ZA
58
or
i
45V
4.39 In the circuit below, find v0 (in V).
IT
i
Et E
g
o
59
r