Lab Report Day Nine - Non-Ideal Power Sources, Maximum Power Transfer

1. Non-Ideal Power Sources

At first, we do a pre-lab finding the power of a source when it is ideal and not ideal.

We find that when we assume it is ideal, there is no internal resistance. We find that the current across it is 0.0455 A. And the voltage across it is being set to be 1 V. Thus, the power is just P=VI= 0.0455 W. 

Then, we consider there is an internal resistance. We calculate the current to be 1/(22+Rs). We calculate the output Voltage is 22/(22+Rs). So the Power of it is 22/(22+Rs)^2 W. 

 

 

We measure the 22 ohm resistor to have a real value of 22.4 ohm.

Since this is not an ideal power source, when we want it to have 1 V, it only gives 0.994 V. 

We adjust it to be exactly 1.0 V.

In the circuit, the output voltage we have is 0.980 V. 

This is a very easy set-up.

 Then, we use a 39 ohm resistor, and measure it true value to be 38.8 ohm. 

The output voltage for the 38.8 ohm resistor is 0.993 V. 

 

Summary of Our Results

 

When we measure the 22.4 ohm resistor values, we get a output voltage of 0.980 V. Based on our calculation, we find the internal resistance to be 0.457 ohm.

When we measure the 38.8 ohm resistor values, we get a output voltage of 0.993 V. Based on our calculation, we find the internal resistance to be 0.273 ohm.

It makes sense because the bigger value the resistor has, the smaller influence the internal resistor would act on it. When the resistance is way bigger than the internal resistance, we can just ignore the internal resistor. 

 

 2. Maximum Power Transfer

We first do a pre-lab on Maximum Power Transfer. We use two identical resistors in the circuit with theoretical values of 2.2K ohm. We calculate the theoretical power of it to be 2.84*10^-3 W. 

We take 5 resistors with theoretical values of 2.2K, and take 2 of them that has same true value of 2.16 K ohm.

This is the set up of this experiment. This is also a simple setup. We measure the voltage across it to be 2.48 V. And we calculate the experimental value to be 2.847*10^-3 W. It has a -0.246 % difference. It is very close to our theoretical value.

 

Summary:

Today, we learn Norton's theorem and maximum power transform. Norton’s theorem is just like Thevenin’s Theorem, except that it replace the circuit with a current source in parallel with a resistor. It is important to transfer maximum power to the load. In order to do that, the load resistance should equal the Thevenin resistance. We also learn that power sources contain an internal resistance and how to calculate the resistance.