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Lecture03 DC circuit Solutions

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ERA100
ElKunsksp-grundkurs
Dr. Maher Azaza
EST
[email protected]
22-01-2017
1
Lecture 03: Blandade Övningar
Plan
1. Exercices
• Thevenin’s Theorem
• Norton’s Theorem
• Thevenin-Norton Conversions
• Maximum Power Transfer Theorem
• Superposition method
2
DC circuit Analysis: Mesh Analysis
The Mesh Current Method, also known as the Loop Current Method, that it
uses simultaneous equations, Kirchhoff’s Voltage Law, and Ohm’s Law to
determine unknown currents in a network.
The first step in the Mesh Current method is to identify “loops” within the
circuit encompassing all components. In our example circuit, the loop
formed by B1, R1, and R2 will be the first while the loop formed by B2, R2,
and R3 will be the second.
The choice of each current’s direction is entirely arbitrary, just as in the
Branch Current method, but the resulting equations are easier to solve if the
currents are going the same direction through intersecting components (note
how currents I1 and I2 are both going “up” through resistor R2, where they
“mesh,” or intersect). If the assumed direction of a mesh current is wrong, the 3
answer for that current will have a negative value.
DC circuit Analysis: Mesh Analysis
The next step is to label all voltage drop polarities across resistors according to
the assumed directions of the mesh currents. Remember that the “upstream”
end of a resistor will always be negative, and the “downstream” end of a
resistor positive with respect to each other, since electrons are negatively
charged. The battery polarities, of course, are dictated by their symbol
orientations in the diagram.
Using Kirchhoff’s Voltage Law, we can now step around each of these loops
4
DC circuit Analysis: Mesh Analysis
Direction of the arrow
from negative to positive
Tracing the left loop of the circuit, starting from the upper-left corner and
moving counter-clockwise
SINCE THE DIRECTION OF THE VOLTAGE IS
OPPOSITE TO THE DIRECTION OF CURRENT ON THE LOOP
If we trace the other loop of the circuit, we can obtain another KVL equation
-7 +2(I1+I2) + 1I1=0
5
DC circuit Analysis: Exercises
Exercises 01
6
DC circuit Analysis: Exercises
Exercises 01
7
DC circuit Analysis: Exercises
Exercises 02
8
DC circuit Analysis: Exercises
Exercises 02
9
DC circuit Analysis: Exercises
Exercises 03 : Answer: Req=10 Ohm
Exercises 04 :
10
DC circuit Analysis: Exercises
Exercises 05 : Answer: Req=19 Ohm
Exercises 06:
11
DC circuit Analysis: Exercises
Exercises 06:
12
DC circuit Analysis: Exercises
Exercises 07:
(a) original Delta network, (b) Y equivalent network.
13
DC circuit Analysis: Exercises
Exercises 08:
(b) resistive circuit equivalent model.
14
DC circuit Analysis: Exercises
Exercises 08:
15
DC circuit Analysis: Exercises
Exercises 09:
16
DC circuit Analysis: Exercises
Exercises 09:
17
DC circuit Analysis: Exercises
Exercises 09:
18
DC circuit Analysis: Exercises
Exercises 10:
19
DC circuit Analysis: Exercises
Exercises 11:
20
DC circuit Analysis: Exercises
Exercises 13:
No current is circulating in the 1 ohm resistor so we have : Vth=Vab= V(resistor 12)
21
DC circuit Analysis: Exercises
Exercises 13:
22
DC circuit Analysis: Exercises
Exercises 14:
23
DC circuit Analysis: Exercises
Exercises 14:
24
DC circuit Analysis: Exercises
Exercises 15:
25
DC circuit Analysis: Exercises
Exercises 15:
26
DC circuit Analysis: Exercises
Exercises 15:
27
DC circuit Analysis: Exercises
Exercises 12:
28
DC circuit Analysis: Exercises
Exercises 12:
29
DC circuit Analysis: Exercises
Exercises 12:
30
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