SEE 1023 Circuit Theory Prepared by : jaafar shafie Superposition Examples.
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Transcript of SEE 1023 Circuit Theory Prepared by : jaafar shafie Superposition Examples.
SEE 1023 Circuit Theory
Prepared by : jaafar shafie
Superposition
Examples
Superposition Principle
The superposition principle states that the voltage across an element in a linear circuit is the algebraic sum of the voltage across that element due to each independent source acting alone.
The superposition principle states that the current through an element in a linear circuit is the algebraic sum of the current through that element due to each independent source acting alone.
OR
Superposition Principle
60V
6A
+ Va -
8
8
4
8
6
8
Ia
1. Find Va and Ia
Superposition Principle
1. 60 V Acting alone
R2
8
2.500A
-
R7
41.250A
+
R10
8 2.500A
-20.00V
R9
8
625.0mA
20.00V
V160V
2.500A
0
25.00V
I10
0A
R1
6
2.500A
R8
8625.0mA
v
20.00V
Va1 = -20V
Ia1 = 625mA
Superposition Principle
2. 6A Acting alone
Va2 = 16V
Ia2 = 500mA v
16.00V
32.00V
R1
62.000A
28.00V
R7
41.000A
R8
8500.0mA
0
R9
8
500.0mA
+
R2
8
4.000A
I16A
6.000AR10
82.000A
V10
2.000A
32.00V
-
Superposition Principle
3. The whole Circuit
Va = -4V
Ia = 125mA
R9
8
125.0mA
-
52.00V
52.00V
R8
8125.0mA
0
53.00V
+
R10
8 500.0mA
-4.000V
R1
6
500.0mA
I16A
6.000A
R2
8
6.500A
R7
4250.0mA
v
V160
500.0mA
Superposition Principle
2. Find Va and Ia
- Va +2Vx
8 4
6
8 Ia
60V 6A
-+
-Vx
+
6A60V
Superposition Principle
1. 60 V Acting alone
18.46V
R2
8
5.385Aa
V160
6.923A
0
12.31V
0V
+
-
60.00V 43.08V
R3
4
1.539A
v
R1
6
6.923A
I10
0A
E1
-2*V(a)
5.385A+ -
R4
8
1.539A
+-
Va1= -41.54 V
Va1
Ia1= -5.385A
Superposition Principle
2. 6 A Acting alone
+-
Va2= 11.08 V
Va2
Ia2= -3.231A
0V
00V
I16A
6.000A
R3
4
923.1mA
V10
1.846A
R2
8
3.231A
v7.385V
+
11.08V
R4
8
923.1mAa
-
R1
6 1.846A
25.85VE1
-2*V(a)
2.769A+ -
Superposition Principle
3. The Whole Circuit
+-
Va = -30.46 V
Va
Ia = -8.615A
a
I16A
6.000A
29.54V
R4
8
2.462AR2
8
8.615A
0
-
60.00V
V160V
5.077A
R3
4
2.462A +
68.92V
19.69V
v
R1
6
5.077A
E1
-2*V(a)
2.615A+ -
0V
CHAPTER 2: Tutorial
1. Use superposition to find Vo
25 V5 mA
2.2Ix
4 k
20 k
+
-
Vo
Ix
CHAPTER 2: Tutorial
2. Use superposition to find Vo
8 V2 A
3Ix
6 3
Ix
+
-
Vo+ -
CHAPTER 2: Tutorial
3. Determine the maximum power delivered to the variable resistor R. (4-70)
40 V
Vx
3Vx
-+
6
5 5
15 R
CHAPTER 2: Tutorial
4. What resistor connected across terminals a-b will absorb maximum power from the circuit? What is that power? (4-71)
8 V
120Vo
3 k
1 k
10 k
40 k-
+
+-
Vo
a
b
CHAPTER 2: Tutorial
6. Determine the maximum power that can be delivered to the variable resistor R. (4-73)
60 V
10
20 5
25 R
CHAPTER 2: Tutorial
7. Determine the value of R such that the maximum power delivered to the RL is 3 mW (4-75)
1 V 2 V 3 V
R
R
R
RL
CHAPTER 2: Tutorial
8. Assume RTh can be varied while RL is fixed at 10 . what is the value of RTh so that maximum power can be transferred to RL. What is that power?
20 V10
RTh
CHAPTER 2: Tutorial
9. Compute the value of R that results in maximum power transfer to the 10 resistor. Find that maximum power.
12 V10
R
8 V
20
