#### Transcript of NODAL ANALYSIS

GROUP MEMBERS NAME

1) SITI NOOR FATIHAH BT AHMAD

AE 130033

2) RATHY-SHRY A/P VELOO

AE130287

3) NURUL AFNEE BT ABDUL AZIZ

AE130066

INTRODUCTION

In electric circuits analysis, nodal analysis, node-voltage analysis, or the branch current method is a method of determining the voltage between "nodes" in an electrical circuit in terms of the branch currents.

1) Every circuit has n nodes with one of the nodes being

designated as a reference node.

2) We designate the remaining n – 1 nodes as voltage nodes

and give each node a unique name, vi.

3) At each node we write Kirchhoff’s current law in terms

of the node voltages.

4) We form n-1 linear equations at the n-1 nodes

in terms of the node voltages and solve the equation by making the calculation.

v1-v2

R2

+

v1-v3

R3

=

I

1

v2-v1

R3

+

v2

R4

+

v2

R5+R6

=

0

v1

R1+R2

+

v1-v2

R3

=

I1

v2-v1

R3

+

v2

R4

+

v2

R5+R6

=

0

Steps 1 and 2 have already been applied. To apply step 3:

In this case there is only one unknown, vb. Plugging in numbers and solving the circuit we get

EXAMPLE 1

EXAMPLE 2

The first part of the problem involved obtaining these equations:

I'm going to solve this problem using Cranmer's Rule, but either the Gauss elimination method or matrix inversion will work equally as well.

So, the two node voltages are:

Now, we set this up in matrix form:

So. the answer will be:

Based on the analysis of the circuit, we have these two nodal equations.

Put into a matrix gives:

Solved using Cranmer's method.

So, the node voltages are:

Looking at the circuit again, v can be found simply by subtracting node 2 from node 1

EXAMPLE 3

Lecturer Muhammad Shukri bin Ahmad

**NODAL ANALYSIS**

BASIC CIRCUIT: THE CONCEPT

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