Thevenin Equivalent

According to the very interesting thevenin theorem, every single circuit could be reduced to a power supply and a resistor. To grasp the concept we did the following lab experiment. In the given circuit, we are interested in information about the R_L2 resistor, so we reduce everything else to an equivalent voltage source and resistor called V thevenin and R thevenin respectively.

 Assuming the following information are given we will try to solve the problem.

R_C1 = 100Ω ,R_C2=R_C3=39Ω , R_L1=680Ω and V_s1=V_s2=9V

  If we short the circuit where R_L2is then we can solve for the voltage at the main junction and find the I through R_C3.

 

At that junction:

 I_SC being the current through Rc3 and Vy the voltage at the main junction.

Now to find R thevenin we break the circuit at R_L2.

 

 Using node voltage analysis at the same junction as before gives: 

 now we can find the thevenin resistance:

Given that  V_{Load2, min}= 8V we can determine smallest acceptable RL2.

 

Now that we have all the values we do the same experiment through 2 different setup. One we will use all the initial elements given and the second time we use the thevenin voltage and resistance equivalent. 

First we construct the circuit with thevenin equivalents. But before we start we have to measure the actual value of the resistors and thevenin voltage.

Again for both parts we used the variable voltage sources in order to get as close as possible to the nominal value.

Component measurements for the second setup is as follow:

 

 This table also shows that the power increases at first but after reaching R_L2  = R_Th  starts decreasing again. Finally we can say with certainty that we can change any complicated circuit with its thevenin equivalent.