This document provides an overview of the concepts of Kirchhoff's voltage law (KVL), Kirchhoff's current law (KCL), and nodal analysis that will be used in a lab involving circuit simulation and calculations. It includes: - An outline of the lab activities over two weeks involving building circuits in Multisim, measuring voltages and currents, verifying KVL and KCL, and performing nodal analysis calculations. - Explanations and examples of KVL, KCL, wye-delta transformations, and the definitions of current entering and leaving a node in nodal analysis. - Examples of applying KVL and KCL to analyze simple circuits and setting up the nodal

1. KVL, KCL and Nodal
Analysis

2. Lab #3 Overview
 First Week
• Simulation using MultiSim (see Multisim.ppt)
• Wye-Delta calculations
• Activity #2 – Build circuit
• Measure voltages, calculate currents
• Verify KVL (through step 10 of Activity #2)
 Second Week
• Activity #2 – Build same circuit
• Verify KCL
• Change source voltage
• Activity #3 – Modify circuit using Delta-Wye
• Nodal Analysis Calculations

3. Multisim Window

4. R1
R2
R3
c a
b
c a
b
Rc
Ra
Rb
Delta or D Wye or Y
R
R R
R R R
R
R R
R R R
R
R R
R R R
a
b
c

 

 

 
1 2
1 2 3
2 3
1 2 3
1 3
1 2 3
Wye-Delta Transformation
R
R R R R R R
R
R
R R R R R R
R
R
R R R R R R
R
a b b c a c
b
a b b c a c
c
a b b c a c
a
1
2
3

 

 

 
Y to Δ Equations Δ to Y

5. Kirchhoff’s Voltage Law, KVL
3 V
R1
2.2 k
R2
3.7 k
R4
5.4 k
R3
1.0 k
1 2 3
0
+ VR1
- - VR2
+
-
VR4
+
-
VR3
+
Loop (0, 1, 2, 0)
V0,1 + V1,2 + V2,0 = 0 V
-3 V + VR1 - VR3 = 0 V
Loop (0, 3, 2, 0)
V0,3 + V3,2 + V2,0 = 0 V
VR4 + VR2 - VR3 = 0 V
For example:
V1,2 = - V2,1 = VR1

6. Nodal Analysis 1
entering
leaving
A current is entering the node if the current is leaving the device.
A current is leaving the node if the current is entering the device.

7. Nodal Analysis 2
Apply Ohm’s Law (I = V/R) for R1:
current entering node 2 = (V1 - V2) / R1
current leaving node 2 = (V2 - V1) / R1
R1
1.5 k
1 2

8. Kirchhoff’s Current Law, KCL
KCL at node 2:
 
I I
I I I
V V V V V V
entering leaving
R R R

 





1 3 2
1 2 0 2 2 3
2 2 1 3
. k .0 k .7 k
Shade indicates a node
At node 1, V1=3 v. due to source
At node 0, V0=0 v. due to ground
KCL at node 3:
V V V V
2 3 3 0
3 7



. k 5.4 k
3 V
R1
2.2 k
R2
3.7 k
R4
5.4 k
R3
1.0 k
1 2 3
0
IR1
IR2
IR3
IR2
IR4

9. Nodal Analysis
Shade indicates a node
3 V
R1
2.2 k
R2
3.7 k
R4
5.4 k
R3
1.0 k
1 2 3
0
IR1
IR2
IR3
IR2
IR4
Substitute the known voltages into the equations that were obtained at nodes 2 & 3
Solve the two equations for V2 and V3
You can put the two equations in matrix form and solve using Matlab or any
mathematics program (or your calculator).