Thevenin's Theorem

In this lab, we are introduced to the fourth way to analyze a circuit. The first one we covered is nodal analysis. The second one is mesh analysis. The third one is superposition. Thevenin's theorem is not similar to any of the above three methods. It neither does divide-and-concur strategy to the circuit calculation by looking at nodes or meshes, nor removes the power sources to simplify each case. The way it works is to replace everything in the circuit with a simple voltage source and a equivalent resistor except for the load.

Here is the circuit graph

In the first picture, we showed our calculation the Rth by removing all the power sources in the same way as superposition method. The we can get the equivalent of the resistors that are left over.

In the second picture, we found the Vth across the load by using mesh analysis. we found the current of each mesh and use them to calculate the potential difference across the load. The theoretical values are listed on the board.

Then we did an experiment based on this circuit. We measured the resistance of the resistors we would use.

After we constructed the circuit, we measured the Rth and Vth

We compared the experimental data and the theoretical data

	Experimental	Theoretical	Percent Error
Thevenin Voltage (V)	-0.46	-0.46	0.76%
Thevenin Resistance (kΩ)	7.61	7.70	1.15%

It turns out that the lab results have very small percent error. We can say that it supports the Thevenin's theorem. 

Summary:

Thevenin's theorem is a very convenient way of studying circuit when only one element of the circuit is considered as a variable. It works the best when the value of a resistor is changing. It might take more time to calculate once, but it does not require any re-calculation even if the value of the load is changed. It is inevitable to redo the calculation if we use mesh analysis or node analysis. The disadvantage is that dependent sources will make the Thevenin theorem a lot more complicated. An extreme case would be that all sources are dependent sources. The Thevenin voltage would be very hard to calculate. Even if it does not work the best for every single problem, it is a useful technique overall.