Superposition II

In this lab, we are introduced to the third circuit analysis method, superposition method. It considers the current through or the voltage across an element to be a combination effect of every single source. Its essence is to turn on one power source at a time to calculate the current of voltage while the others are kept off. Then it switches to a another power source until every one of them is turned on once. The actual current or voltage will be the mathematical addition of the current or voltage of each case.

Here is the circuit graph

The circuit on the top is the actual circuit before the use of superposition method. The one at the bottom left is the configuration of the circuit with the 5V source replaced by a short circuit. The one at the bottom right is the configuration of the circuit with the 3V source replaced by a short circuit. The theoretical voltages for each case is 0.708V and 1.99V, respectively. The combined voltage is 2.70V.

We constructed the circuit based on the two cases.

3V on, 5V off

3V off, 5V on

Both 3V and 5V on

We also measured the resistance of the resistors under different cases

We put all the data in a table and compared the experimental values and theoretical values

	Experimental	Theoretical	Percent Error
voltage from 3V	0.70	0.708	1.13%
voltage from 5V	1.99	1.987	0.15%
voltage from both	2.70	2.695	0.19%

Theoretical Resistor (k Ω)	Measured Resistor (kΩ)
1	0.96	± .01kΩ
4.7	4.65	± .01kΩ
10	9.95	± .01kΩ
6.8	6.77	± .01kΩ
22	21.2	*±.1 kΩ

The percent errors are really small. The lab result successfully verifies the validity of superposition method.
We simulated the same circuit on everyCircuit app and it shows the same result.

Summary:
Superposition method is a very useful way to analyze circuit when there are multiple power sources in different places. If removing all power sources but one can make the circuit very easy, this would be the best way to analyze. We remove current source by using open circuit and voltage source by short circuit. However, this method has a significant flaw. We have to do a calculation of the whole circuit for each turned on source. An additional power source can significantly increase the amount of work. Additionally, removing a power source does not always simplify the circuit very much when they are close to each other.

This method reminds me of the composition of waves. The way the superposition method works resembles the constructive interference and destructive interference. Current is the movement of electrons. Electrons are not only particles, but also waves. A traveling wave can mix with another traveling wave and create a combined effect in the same way as the mathematical addition of two current values.