Thevenin Equivalents

For Thevenin Equivalents, we are given a circuit and want to know how a change in one element (Rl2) affects the circuit as a whole. We can simplify this calculation by reducing everything else in the circuit to an equivalent Thevenin resistance and voltage.


The first step involved calculating Vth, which we were able to do with nodal analysis. We open-circuited the terminals across Rl2 and found the voltage in a parallel element.


Vth = 8.64 V


We then open-circuited the terminals across Rl2 and found the current flowing through. We could then put this current and Vth together in Ohm’s Law to find the Thevenin resistance, Rth. As a check, we solved for Rth using the parallel/series equivalent resistance method.


I = 0.131 
Rth = 65.9 Ohms


With the circuit now simplified to three elements (Vth, Rth, and Rl2), we calculated the Rl2 corresponding to the minimum voltage (8V) allowed across this element. We then solved for the short-circuit current and open-circuit voltage.


Rl2min = 823.75 Ohms
I = 0.009711 A
V = 8V


Next, we put together the circuit. We used a voltage supply for Vth, a resistor box set to 66 Ohms for Rth, and another resistor box for Rl2. We measured the voltage across the load for two cases: one where Rl2 = Rl2min and one where Rl2  = infinity (an open circuit).

The Thevenin circuit 

These were our measurements:

Config	Theoretical	Measured	% Error
Rl2=Rl2min	8V	7.59V	5.12%
Rl2=infinity	8.64V	8.47V	1.97%