Thevenin's Good Idea - Session 2

Date: 2/3/15       Lab Partner: Camille

Thevenin's Good Idea - Session 2

Section 1 - What Makes a Motor Spin

This lab starts with an exploration of the LEGO motor. We power the LEGO motor, first from the 5V Arduino pin and take a rough estimation of the torque by stopping the arm of the motor with our finger at the very end of the arm. We then shift the power source from the 5V pin to an output pin whose output voltage is set to 5V. We again take a rough estimation of the torque in the same manner as before. The torque under this stall condition was weaker when the source was from the output pin than it was when the source was the 5V pin. This confirms what the lab outline tells us that "the output pins on the Arduino are not very good at powering a LEGO motor, compared to the 5V power line." This difference has to do with the amount of current supplied by the Arduino chip.

Section 2 - The Thevenin Model

The Thevenin's Theorem says that you can model any circuit as an equivalent circuit called the Thevenin Model that consists of only one Thevenin voltage source and one Thevenin resistor. This allows complicated circuits to be abstracted into a black box with just a Thevenin equivalent voltage and resistance that can be used to calculate the output of the circuit, which is relevant when you want to connect circuits.

  Subsection A - The Thevenin equivalent of a power supply

  When we construct a circuit of just 5V and a 47Ω resistor and take the measurements of 4.95V across the power and ground busses without a resistor and of 4.76V with the resistor, we can calculate the approximate equivalent Thevenin voltage of 4.95V and resistance of 2Ω.

  Subsection B - The Thevenin equivalent circuit of an Arduino digital output pin

  We programmed one of the Arduino output pins to be a high voltage (5V) and using it as the voltage source, applied the same process as above to measure 4.95V without the resistor and 2.84V with the resistor. We then calculated the Thevenin equivalents to be 4.95V and 35Ω.

  Subsection C - The Thevenin equivalent circuit of a LEGO motor

  This time, we connected a LEGO motor to our circuit and made the measurements when while we stopped the LEGO arm from moving by pushing it down with a finger. We calculated the Thevenin equivalent voltage to be 4.95V and the equivalent resistance to be 35Ω. As a check of our work, we directly measured the resistance between the two pins of the motor and found it to be 28Ω. This is close to our calculated 35Ω.

**Fun aside** Motors also function as generators, and we demonstrated this by connecting a LEGO motor directly to an oscilloscope. We then spun the arm of the LEGO motor and noted that it produced voltage changes that could be seen on the oscilloscope. Very cool! You can see it in the video below.

Section 3 - The Voltage Divider (Lab 1-4 in Student Manual)

To demonstrate the concepts of voltage dividers we built a circuit with two 10kΩ resistors in series with a 5V power source from the 5V pin. We measured the open circuit output voltage to be 4.96V and the voltage when a 10kΩ load is added to be 1.69V. 

Then we measured the short circuit current to be 0.5mA and you can see this in the picture below.

From the short circuit current measurement and the open circuit voltage measurement we calculated the Thevenin equivalent circuit to consist of a 2.5V power source and a 5kΩ resistor. We then built this equivalent circuit with variable regulated DC supply set to give 2.5V and a 4.7kΩ resistor which is approximately the same as the 5kΩ especially given the 10% margin of error for resistors. We measured the short circuit current and open circuit voltage of this new circuit and found it to be the same as the voltage divider circuit, confirming that the new circuit is a Thevenin equivalent. We also confirmed the measurements with a 10kΩ load. The 10kΩ resistor in series with the 5kΩ produced a voltage drops of (2.5V/3) 0.83V and (2*2.5V/3) 1.66V which is proportional to the resistors with (10/15)2/3 and (5/15) 1/3. You can see this confirmed in the Thevenin equivalent circuit in the picture below and it matched the result from the voltage divide circuit.