Day 5- Nodal Anylysis

In-order to construct a reliable power system for military usesage, the system must contain two power sources so when ever one of the source broke down the other back up source will still functioning the system.
Consider the schematic shown below

We can use nodal analysis to find the current went into and when out from the notes in-order to determine the suitable value for the voltage supplies

We can first establish the nodal equatinos in terms of the variable v1 and v2

(v1-v2)/100=v2/100 + (v2-v3)/220

(v2-v3)/220+ (v4-v3)/220=v3/1000
where v1 is 12V   v2 is 9v

we obtained V2=10.26V   V3=8.67V

Next, we can calculate the corresponding current leaving each battery
I_batt1= (12-10.26)/100=0.0174
I_batt2=(9-8.67)/220=0.0015


Then we can calculate the power supplied by each battery
P_batt1=0.2088W
P_batt2=0.0135W


Next, we devise the experiment to measure the battery current and the unknown node voltages

Data of the component

 

Component	Nominal Value	Measured Value	Power Rating
R_C1	100+-5%	98	1/4W
R_C2	220+-5%	248	1/4W
R_C3	220+-5%	222	1/4W
R_L1	100+-5%	987	1/4W
R_L2	100+-5%	981	1/4W
V_bat1	12V	12.08	24W
V_bat2	9V	9.01	18W

Data obtained from the experiment

Variable	Theoretical Value	Measured Value	Percent Error
I_bat1	0.0174A	17.12mA	1.60%
I_bat2	0.0015A	1.77mA	18%
V2	10.26V	10.34V	0.78%
V3	8.67V	8.33V	1.15%

We can see that our results are really close to our theoretical value within 5%. The only number that is off is I_bat2. The possible explanation should be lack in accuracy in our device. If we could get another multimeter that can read one more digits in the current, we will be able to decrease the percent Error significantly.



Next we can do some calculation to find the power delivered by the two batteries
P_bat = -0.2068W
P_bat2=0.01625W


Next, assume that we want V2=V3=9V, use the nodal equations derived in the previous part to find the required battery voltages

By solving the same equation, we are able to obtain that V1=10.98V
V2=9.9V

To do this experience, we need to replace the power supply with a variable power supply. The main difference of the power supply is that we are able to change the output voltage to any number within its limitation

From this

to these

This is one of the power supply that is provided in class. We used this power supply before for physics 4B, and the result is terrible due to the old technology it has. The output voltage is not constant but wondering around +-.5VFor another power supply, we found another one that is more modern and its more precise.

we obtain V2=8.92V  V3=8.8V  I_bat1=9.29mA I_bat2=8.03mA

Even thought the numbers are not close, but the percent errors in the voltage are all within the five percent. This experiment demonstrated the use of nodal analysis.