17-Mar-2016: Day 8

Exercise 1:

The opening topic of the day is Thevenin's Theorem which states that any combination of voltage sources and resistors may be replaced with a single equivalent voltage and a single resistor connected in series with the ends open. The voltage across the open ends of the circuit is the same as the new voltage source value, the Thevenin voltage.

Below we ran a practice example to use the theorem. The variable resistor on the far right may be removed temporarily and the circuit left open. Voltage sources may be replaced with short circuits and current sources may be removed all together. This will help in solving the Thevenin resistance.

Below is what the new circuit can be drawn as, where any load resistor can be simply added in series in order to solve for voltage drops due to the loader.

Exercise 2:

A trickier problem, as seen below can require source transformation to reach a central element.

Exercise 3:

Lab:
"Thevenin Circuit Lab"
Given the circuit below, we are to solve for the Thevenin resistance and voltage in order to create a Thevenin circuit. After only 4 failed attempts at solving for the voltage, nodal analysis made our lives much more happy.

Theoretical

Rth = 7.4 kilo-Ohms 

Vth = 0.46 V

Once solved for, we will want to build and measure for the same values in order to compare them with our theoretical ones. To measure the equivalent resistance we must short circuit the voltage sources and measure across the open ends of the circuit.

Measured

Rth = 7.63 kilo-Ohms

Vth = 0.437 V

Now, what if we add the variable resistor, potentiometer in this case? Well, we hypothesized that if a resistance equaling the Thevenin resistance, 7.4 kilo-Ohms, were added to the circuit, then the voltage drop across that resistor would be exactly half of our Thevenin voltage.

Haza! we were correct.

Exercise 4:

Last extra topic of discussion was the Norton equivalent circuit... essentially the source transformation of the Thevenin equivalent circuit.