Thevenin's Excellent Idea

Thévenin’s theorem says that:

•  A DC circuit, with voltage, current sources and resistances, can be replaced by an equivalent voltage source V_th in series connection with an equivalent resistance R_th.

•  V_th – equivalent voltage obtained with terminals A and B open-circuited.
• R_th – equivalent resistance obtained with all the current sources open-circuited and all voltage sources short circuited. 

R_th = V_th / ISC 

The whole idea of Thevenin's good idea is that, we can solve a complex circuit by modeling it into a simpler one.  A very good idea indeed! 
In today's lab we explored a number of simple DC circuits to explore the goodness of Thevenin's idea. I first connected a LEGO motor directly between the power and ground busses and to no-one's shock the blade started rotating. I also felt the torque by stalling the blade with my finger and it was pretty strong. 

Thevenin equivalent circuit of a battery pack:

Using an oscilloscope I found the voltage Vout between the power and ground busses to be 4.2 V. After connecting the 47 ohm resistor, the Vout became 4.1V, a very small drop, which qualitatively gives the idea that the internal resistance of the battery pack is much smaller than 47 ohm. For this circuit,
V_th = 4.2 V
ISC  = 4.1V/47ohm = 87mA
R_th = 4.2 V/0.087A = 48.3 ohm
Internal resistance of battery pack, r = 1.3 ohm

Thevenin equivalent circuit of a LogoChip output pin:
Again, using an oscilloscope I found the voltage Vout between the LogoChip output pin and ground busses to be 4.8 V (new battery pack used). After connecting the 47 ohm resistor, the Vout became 1.9V, which qualitatively gives the idea that the internal resistance of the LogoChip is a little bigger than 47 ohm. For this circuit,
V_th = 4.8 V
ISC  = 1.9V/47ohm = 40 mA 
R_th = 4.8 V/0.04A = 120.0 ohm
Internal resistance of LogoChip, r = 72.5 ohm

Thevenin equivalent circuit of a LEGO motor:
Again, without the motor Vout is 4.7 V. After connecting the motor and stalling it with finger, the Vout became 1.2V, which qualitatively gives the idea that the internal resistance of the motor is of the same order of magnitude as that of the LogoChip. For this circuit,
V_th = 4.7 V
Voltage drop across LogoChip = 4.7-1.2 = 3.5 V
I  = 3.5V/72.5 ohm = 48 mA
Rth = 4.7 V/0.048A = 97.9 ohm
Internal resistance of motor, r = 26 ohm

Student Manual lab 1-4 Voltage Divider

I constructed a voltage divider like the circuit shown above using 3 AA batteries instead of the 15 V suggested voltage. The output voltage across the 10k resistor was 2.33 V. After connecting a 10k load, i.e. another 10k resistor in parallel, the output voltage dropped to 1.53 V. This makes sense, because the effective voltage of the parallel resistors is now 5k, so there is a 1/3rd potential drop across it and a 2/3rd potential drop across the 10k in series. 

where, Rload is 10kohm, Rth is 5 kohm, and Voc or Vth is 2.33 V.
To prove this, by measurement,
ISC  = 0.46 mA
V_th = 2.33 V
therefore,
R_th = 2.33 V/0.46 mA = 5.07 kohm