Basic Electrical Circuits & Machines (EE-107)

Course TeacherShaheena Noor

Assistant ProfessorComputer Engineering Department

Sir Syed University of Engineering & Technology.

Basic Nodal and Mesh analysis

In this chapter, we introduce two different ways to view electric

circuits.

Basic Nodal and Mesh Analysis

• Nodal Analysis:– It is based on KCL.

• Mesh Analysis:– It is based on KVL.

• Both methods allow to construct equations for a wide variety of circuits.

Nodal Analysis

Method:• Use when (normally) multiple sources are

present.• Convert voltage sources into current sources.• Identify all the nodes and choose a reference

node.• All the nodes (except reference node) are

then numbered and their corresponding voltages are designated. V1, V2, . . .

Steps:1. We will assume V1 > V2 > V3... > 0.2. Draw an arrow beside each passive component (resistor)

showing the direction that current flows through it (made on the assumption made in step 1. For example)

3. The arrow is drawn from V1 towards V2, because current

always flow from the higher voltage node to the lower voltage node.

4. Label each arrow with the current it represents, expressed in term of node voltages.

5. Write KCL at each node and solve the equations

Nodal Analysis

V1

10 Ohm

V2

V1

10 Ohm

V2

• For the circuit given below, compute the voltage across each current source.

Nodal AnalysisDrill Problem 4.1 (Page 71)

4A5 Ohm2A

7 Ohm

V1

3 Ohm

V215 Ohm

• For the circuit given below, compute the voltage across each current source.

Nodal Analysis(Drill Problem 4.2) Page 74

7A

Reference Node

4 Ohm1 Ohm

3 Ohm 5 Ohm3A

2 Ohm

Mesh Analysis• Mesh analysis requires that all the sources in a

circuit be voltage source.

• The next step is to draw closed loops in the circuit, each loop representing a path around which KVL will be written.

• The direction of each loop is arbitrary. • It may be either clockwise or counter clockwise.

Mesh Analysis• It is convenient to think of each loop as

representing a current that flows around the loop and we designate each by an appropriate symbol I1, I2 and so on.

• These loop currents are the unknowns in the set of simultaneous equations that results when KVL is written around each loop.

• Thus the number of unknown (loop currents) is the same as the number of equations.

Mesh AnalysisDrill Problem 4.5 (page 80)

• Determine i1 and i2 in the circuit shown below.

14 Ohm

5 Ohm

i1

10 Ohm

6V5V

i2

5 Ohm

Mesh AnalysisDrill Problem 4.6 (page 80)

• Determine i1 and i2 in the circuit given below:

5 Ohm

10 Ohm3V

10V

4 Ohm

i1

7 Ohm

i29 Ohm

1 Ohm