Basic Electric Circuit Analysis Using Nodal Method

Basic Electric Circuits – © 2020 Mouli Sankaran Email: mouli.sankaran@yahoo.com 2
Session 8A: Focus
 Current Division
◦ Examples
 Basic Nodal Analysis
◦ Nodes and reference nodes
 Nodal Analysis
◦ Example
◦ Solve using Nodal analysis
 Writing KCL Equations
 Example Problems

Resistors in Parallel – Current Division

Resistors in Parallel: Current Division
 The dual of voltage division is current
division.
 The current flowing through R2 is:
 Or
 For a parallel combination of N resistors, the current through Rk

Example 1: Current Division
 Find IL :
Note: This is Example problem 2.17 on page 50, Figure 2.27 in the Ref 2 book (by Irwin)
- 0.25 mA
RPequ = 18k || 9k || 12k = 6k || 12k = 4k
Combine Current sources:
i = (-1 + 4 - 2)mA = 1 mA
i = 1 mA RL = 12 kΩ
-1mA
RPequ
iL
4kΩ
o
o

HW Example 2: Current Division
 Find i1 , i2 and v3 :
Note: This is Practice problem 3.15 on page 63, Figure 3.36 in the Ref 1 book (by Hayt)
i40
100mA, 50 mA and 0.8 V
Done during the Tutorial 4 yesterday!!!

Nodal Analysis

Nodal Analysis … KCL Based
 We begin our study of general methods for methodical circuit analysis by
considering a powerful method based on KCL, namely nodal analysis
 In a nodal analysis, the variables in the circuit are selected to be the node
voltages
 The node voltages are defined with respect to a common point in the
circuit
 One node is selected as the reference node, and all other node voltages
are defined with respect to that node
◦ Quite often this node is the one to which the largest number of branches are
connected

Reference and Non-reference Nodes
 Non Reference Node - It is a node which has a
definite Node Voltage.
◦ Example: Here Node 1 and Node 2 are the Non Reference
nodes
 Reference Node - It is a node which acts a reference
point to all the other node.
◦ It is also called the Datum Node (Node 3)

Types of Reference Nodes
 Chassis Ground - this type of reference node acts a
common node for more than one circuits.
 Earth Ground - when earth potential is used as a
reference in any circuit then this type of reference
node is called Earth Ground.
Chassis Ground Earth Ground

Nodal Analysis: Example
How many nodes are in this circuit?
Which one is preferred as reference node?
3 Nodes

Nodal Voltages
 The voltage of node 1 relative to the reference node is named
v1, and v2 is defined as the voltage of node 2 with respect to
the reference node.
 These two voltages are all we need, as the voltage between
any other pair of nodes may be found in terms of them
 For example, the voltage of node 1 with respect to node 2 is
v1 − v2.
◦ Similarly, voltage of node 2 with respect to node 1 is v2 − v1

Nodal Analysis
 Apply KCL to nodes 1 and 2, by
equating the total current
leaving the node through the
several resistors to the total source
current entering the node
At node v1 :
At node v2 :
Simplifying them:
Find the two unknowns v1 and v2 by solving the above two equations.
v1 = 5 V
v2 = 2 V

Writing KCL Equations
 There is more than one way to write
KCL equations
 Sum up all the current entering the
node and equate it to zero
 or
 This results in all current source
terms on one side (left here) and all
resistor terms on the other side
At node v1 :
At node v1 :

Nodal Analysis: Examples

Example 1: Nodal Analysis
 KCL for node v1 :
 Find the current flowing left to right through 15 Ω :
 KCL for node v2 :  Solution:
Zero current
Note: This is Example problem 4.1 on page 82, Figure 4.2 in the Ref 1 book (by Hayt)

Example 2: Nodal Analysis
 KCL for node v1 :
 Find nodal voltages v1, v2 and v3 :
 KCL for node v2 :  KCL for node v3 :
 By solving these equations:
Note: This is Example problem 4.2 on page 83, Figure 4.4 in the Ref 1 book (by Hayt)

HW Example 3: Nodal Analysis
 Find nodal voltages across current sources 3A and 7A:
They are v1 and v3 respectively:
v3v2v1
5.235 V and 11.47 V
Note: This is Practice problem 4.2 on page 86, Figure 4.5 in the Ref 1 book (by Hayt)
Verify from your solution

Session 8A: Summary
 Current Division
◦ Examples
 Basic Nodal Analysis
◦ Nodes and reference nodes
 Nodal Analysis
◦ Example
◦ Solve using Nodal analysis
 Writing KCL Equations
 Example and Home work Problems

References
Ref 1 Ref 2

Basic Electric Circuit Analysis Using Nodal Method

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