EE 1270: Introduction to Electric Circuits
0
Lecture 7:
Mesh Analysis
Chapter 4
Techniques of Circuit
Analysis: Sections 4.5-4.7
EE 1270 Introduction to Electric Circuits
Suketu Naik
Node, Branch, Loop, Mesh
Node
(current
sum)
1
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
EE 1270 Introduction to Electric Circuits
Suketu Naik
Mesh: More Examples
2
Remember that mesh current represents shared current
within a mesh as you go around the loop
EE 1270 Introduction to Electric Circuits
Suketu Naik
Mesh in an Actual Circuit
3
Can you identify meshes in the above circuit?
EE 1270 Introduction to Electric Circuits
Suketu Naik
Mesh-Current Method
4
Find unknown currents by summing the voltages in a mesh
Example 4.4: a) Find the power for each voltage source
b) Find vo
Step1: Draw Mesh
Currents
EE 1270 Introduction to Electric Circuits
Suketu Naik
Mesh-Current Method
 40  2ia  8(ia  ib )  0
8(ib  ia )  6ib  6(ib  ic )  0
6(ic  ib )  4ic  20  0
10ia  8ib  0ic  0
 8ia  20ib  6ic  0
0ia  6ib  10ic  20
EE 1270 Introduction to Electric Circuits
5
Step2: Write
Mesh-Current
Equations by
Summing
Voltages
around the
Meshes
Passive Sign
Convention
Step3: Solve
Simultaneous
Equations in
Standard Form
Suketu Naik
Mesh-Current Method
6
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
Passive Sign
Convention
Both vol. sources are delivering (generating)
power to the circuit
v0= 8(ia-ib)=8(5.6-2)=28.8 V
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP4.7
7
Find the power associated with the voltage source and the power dissipated in the
8 Ω resistor
Simultaneous Equations:
Solution
p80 V =
p8 Ω =
Passive Sign
Convention
Positive Power means it is consumed (dissipated)
Negtive Power means it is generated (delievered)
EE 1270 Introduction to Electric Circuits
Suketu Naik
Positive and Negative Power
8
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:
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP4.8b
9
Find the power associated with the dependent source
Simultaneous Equations:
Passive Sign
Convention
Solution
p-3vϕ =
EE 1270 Introduction to Electric Circuits
Suketu Naik
Supermesh
10
Circuit with current
source between two
meshes
Combine meshes to
create supermesh
and ignore the
current source
EE 1270 Introduction to Electric Circuits
Suketu Naik
AP4.12
11
Find the power dissipated in the 1 Ω resistor
Simultaneous Equations:
Passive Sign
Convention
Solution
p1Ω =
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example: Transistor Circuit
12
An NPN transistor can be used as an amplifier
EE 1270 Introduction to Electric Circuits
Suketu Naik
Example Fig. 4.27-4.28: Transistor Circuit
13
The transistor circuit can be analyzed using the supermesh
Find iB, iE, and iC if Vcc=15 V, R1=100 kΩ, R2=50 kΩ, Vo=0.65 V,
Rc=10 kΩ, RE=4.25 kΩ, β=300
EE 1270 Introduction to Electric Circuits
Suketu Naik