lecture 7: mesh analysis chapter 4 techniques of circuit...
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ECE 1270 Introduction to Electric Circuits Suketu Naik
0EE 1270: Introduction to Electric Circuits
Lecture 7:
Mesh Analysis
Chapter 4
Techniques of Circuit
Analysis: Sections 4.5-4.7
ECE 1270 Introduction to Electric Circuits Suketu Naik
1Node, Branch, Loop, MeshNode
(current
sum) Mesh
(voltage
sum)
Branch
Node: A point where two or more circuit elements join
Mesh: A loop that does not enclose any other loops
Branch: A circuit path that contains two nodes
Loop: A path with starting node=last node; can contain many meshes
ECE 1270 Introduction to Electric Circuits Suketu Naik
2Mesh: More Examples
Remember that mesh current represents shared current
within a mesh as you go around the loop
ECE 1270 Introduction to Electric Circuits Suketu Naik
3Mesh in an Actual Circuit
Can you identify meshes in the above circuit?
ECE 1270 Introduction to Electric Circuits Suketu Naik
4Mesh-Current Method
Find unknown currents by summing the voltages in a mesh
Step1: Draw Mesh
Currents
Example 4.4: a) Find the power for each voltage source
b) Find vo
ECE 1270 Introduction to Electric Circuits Suketu Naik
5Mesh-Current Method
Step2: Write
Mesh-Current
Equations by
Summing
Voltages
around the
Meshes
0204)(6
0)(66)(8
0)(8240
cbc
cbbab
baa
iii
iiiii
iii
Step3: Solve
Simultaneous
Equations in
Standard Form
Passive Sign
Convention
201060
06208
400810
cba
cba
cba
iii
iii
iii
ECE 1270 Introduction to Electric Circuits Suketu Naik
6Mesh-Current Method
Passive Sign
Convention
ia= 5.6 A
ib= 2 A
ic= -0.8 A
p40V= (40 V)(-5.6 A)=-224 W
p20V= (20 V)(-0.8 A)=-16 W
Both vol. sources are delivering (generating)
power to the circuit
v0= 8(ia-ib)=8(5.6-2)=28.8 V
ECE 1270 Introduction to Electric Circuits Suketu Naik
7AP4.7
Simultaneous Equations: Passive Sign
Convention
Solution
p80 V =
p8 Ω =Positive Power means it is consumed (dissipated)
Negtive Power means it is generated (delievered)
Find the power associated with the voltage source and the power dissipated in the
8 Ω resistor
ECE 1270 Introduction to Electric Circuits Suketu Naik
8Positive and Negative Power
Positive Power means it is consumed by a circuit element,
i.e. vol. source, cur. source, resistor, capacitor, inductor etc
Negtive Power means it is generated (delievered) by a cur. source
or a vol. source
The positive or negative sign depends on the polarity of the voltage
and direction of the current
Q: Where happens to the dissipated or consumed power in a
resistor?
A:
ECE 1270 Introduction to Electric Circuits Suketu Naik
9AP4.8b
Simultaneous Equations:
Passive Sign
Convention
Solution
p-3vϕ =
Find the power associated
with the dependent source
ECE 1270 Introduction to Electric Circuits Suketu Naik
11Supermesh
Circuit with current
source between two
meshes
Combine meshes to
create supermesh
and ignore the
current source
ECE 1270 Introduction to Electric Circuits Suketu Naik
12AP4.12
Simultaneous Equations:
Passive Sign
Convention
Solution
p1Ω =
Find the power dissipated in the 1 Ω resistor
ECE 1270 Introduction to Electric Circuits Suketu Naik
13Example: Transistor Circuit
An NPN transistor can be used as an amplifier