March 19,Thevenin's Theorem

Use of every circuit

Prelab result

Thevenin's resistance is 7.1K

Thevenin's voltage is 0.458V

Thevenin's circuit

If R=1k, I should be 54.4uA

Actual Circuit used in lab

Measured Vth=0.461V, compare to pre-lab value 0.458V, the percentage difference is 0.6%

Measured Rth=7.10K,compare to pre-lab value 7.1K, the percentage difference is 0%.Those two values are exact same. 

we put a 1K resistor between a and b then measured voltage across 1K load resistor, V=0.055V

Then we change the load resistor to 4.7K and measure the voltage across this resistor.V=0.17V

Result table.

For 1K load the theoretical value is 0.457*(1/(1+7.1))=0.056V while the measurement is 0.055V, percentage difference is 1.9% we can say they are same.

For 4.7K load the theoretical value is 0.457*(4.7/(4.7+7.1))=0.182V while the measurement is 0.17V, percentage difference is 3.6%, they are also could be same.

The slight difference may due to the difference in resistance we use.

Then we build the Thevenin's circuit. We use two 3.5K resistors and a 100 resistor connect in series to make a 7.1K resistor. 

Compare original circuit and Thevnin's equivalent circuit

For 1K load the original is 0.055V while the THEQ circuit is 0.054V, the difference is 1.9%, we could say they are same.

For 4.7K load, the original is 0.17V while the THEQ circuit is 0.17V, the difference is 0%, we could say they are same.From the result we examine the Thevenin's equivalent circuit is equivalent to the original circuit.

Data table for the potentiometer. 

The maximum power is when Rl=Rth=7.1K ohm.

P=(V(Rl/(Rl+Rth)))^2/Rl

Theoretically the Pmax=7.48*10^(-6)W. 

From the table the maximum power is 7.58*10^(-6)W when Rl=5600 ohms, which is a little bit off from the expectation. That may due to the inaccurate measurement, since from the graph the point on 5600 seems a outlier. possible we make a mistake when we take the resistance measurement. 

IN the future I could suggest that take more data from potentiometer to create a better graph to see the trend of power change with load resistance change. 

Summary:
In today’s lab, we practice more on Thevenin’s Theorem, and examine that Thevenin's theorem actually work. Also we try to find the max power deliver to the load resistance, based on our experiment, we can see that the power of a load resistance is about constant. It will only change a little bit when the resistance changes.