Nodal Analysis

Introduction

In this lab, we are trying to build a reliable power system by using 2 sources and a couple of circuit breakers. we will be able to isolate the damaged equipment or reconfigure the system. We are using a resistor box for the load on the circuit. The nodal analysis is used in this experiment to calculate the voltage drop across the node. The voltage sources that we're going to use in this experiment are  9V voltage source and 12V voltage source.

Experimental

Component	Nominal Value	Measured Value	Power of Current Rating
RC1	100 Ω	99.1 Ω	0.25 W
RC2	220 Ω	218 Ω	0.25 W
RC3	220 Ω	220 Ω	0.25 W
RL1	1000 Ω	985 Ω	0.25 W
RL2	1000 Ω	986 Ω	0.25 W
VBat1	12 V	12.13 V	2 A
VBat2	9V	9.03 V	2 A

Once all the components has been measured, the circuit is set up as follow:

Once the circuit is made, several data is taken as follow:

Variable	Theoretical Value	Measured Value	Percent Error
IBat1	17.4mA	18.62 ± 0.005 mA	7.01%
IBat2	1.5mA	1.30 ± 0.10 mA	13.3%
V2	10.26 V	10.24 ± 0.01 V	0.194%
V3	8.67 V	8.37 ± 0.01 V	3.46 %
PBat1	208.8 mW	226 mW	8.23%
PBat2	13.5 mW	11.7 mW	13.3%

After the data is taken, the second part of the experiment is conducted where V_1 = V_2 = 9 V. Nodal equation is used and we found that the V_bat1 has to be 9.9 V and V_bat2 = 10.98 V. The setup of the second part is as follow:

Since the voltage in the previous part is unregulated voltage, when it is regulated, adjustment to the voltage source has to be made. The data for it is as follow:

Variable	Value
VBat1	10.3 ± 0.05V
VBat2	11.5 ± 0.1 V
V2	9.13 ± 0.05V
V3	7.83 ± 0.05V
IBat1	10.60 ± 0.005 mA
IBat2	8.10 ± 0.005 mA

Conclusion

      The result obtained has a fairly low percent error with the highest being 13%. This result can be found from several things. One of the reason of this error is the use of 5 resistor which each have a 15% uncertainty. Other reason is that we set the voltage source before we put it in the circuit, so when it is regulated by the circuit, the voltage decrease. We fail to take this into consideration, hence the percent error.