Thevenin Equivalents

Thevenin's theorem allows us to take a complicated system and simplify it down to a voltage source and an equivalent resistance.

We first found the Thevenin resistance and Thevenin voltage of a seemingly complex circuit. Our analysis yielded us values of

V_Th = 8.64 V
R_Th = 65.95 Ω

We then calculated the smallest value of R_L2 (the load resistance) when V_Th = 8 V.

R_L2 = 824.3 Ω

The next step was to take measurements of V_{Load 2}, the load voltage outside of the Thevenin circuit, for the original circuit and its Thevenin equivalent. We took load voltages for the smallest permissible resistance and for an open circuit. The Thevenin equivalent data are as follows:

Config	Theoretical Value	Measured Value	Percent Error
RL2 = RL2,min	VLoad 2 = 8.00 V	8.37 V	4.63 %
RL2 = ∞	VLoad 2 = 8.64 V	9.06 V	4.86 %

For the original circuit:

Config	Theoretical Value	Measured Value	Percent Error
RL2 = RL2,min	VLoad 2 = 8.00 V	8.55 V	6.88 %
RL2 = ∞	VLoad 2 = 8.64 V	9.06 V	4.86 %

At the end, we calculated some values of power supplied to the load resistor:

Config.	VLoad 2	PLoad 2
RL2 = 0.5RTh	2.88 V	0.252 W
RL2 = RTh	4.32 V	0.283 W
RL2 = 2RTh	5.76 V	0.252 W

The table shows that when R_L2 = R_Th, the maximum power is supplied.