3/8/2016 It's a bird! It's a plane! It's...

Today, we introduced the idea of a supernode, which is collapsing multiple nodes into a single point with a constraint equation. This makes nodal analysis easier, simplifying it. The constraint equation is usually the voltage source inside the node, with a voltage of its own. Then, KVL and KCL are applied normally.

The first diagram shows an example of a supernode connecting two nodes and a voltage source. The voltage source on the left is only connected to the ground node directly, so is therefore not useful as a supernode. We identified all the current sources exiting the supernode. Then, we wrote constraint equations over each node, leaving us with a system of 3 equations and 3 variables.

Next, we looked at a different circuit and applied nodal analysis to find the voltage through the top node.

To find the 10% error, we varied the resistor values by ±10%, such that if the voltage is normally
a = (5/10000 - 3/6800 - 5/20000) / (1/10000 + 1/20000 + 1/6800) = -0.718V

The +10% value becomes
a = (5/11000 - 3/7480 - 5/22000) / (1/11000 + 1/22000 + 1/7480) = -0.64356V

And -10% value is
a = (5/9000 - 3/6120 - 5/18000) / (1/9000 + 1/18000 + 1/6120) = -0.64356V

Oddly the  ±10% values were the same. The error is the difference between this new value and the original value, so a = -0.718 ± 0.0744V.

Now, we have to connect this on a breadboard and use the Analog Discovery Digilent to find the values in practice. 

The voltage across a resistor is the sum or difference of the voltage source and v_2, which we're measuring. Measuring amperage, on the other hand, must be connected in series.

  

We emphasized the importance of PSPICE for electrical engineers to do circuit analysis. This tool is a must-have. An online alternative (with a $10 license fee) is Every Circuit.

Where nodal analysis is useful to find voltages, mesh analysis is useful to find current around loops. A mesh is defined as a loop that does not contain any loops within. With mesh current, we identify the mesh currents, apply KVL, and replace voltages with currents. Each loop is directed clockwise by convention; but regardless, they should be consistent. We did a circuit for an example:

And then used Every Circuit to confirm the results:

We also briefly went over Cramer's Rule for solving a system of equations, which was covered in Math 285. And finally, we covered resistor codes, given red-black-orange:

We were taught the acronym to remember the order of colors representing the digits

0 - Bad - Black

1 - Booze - Brown

2 - Rots - Red

3 - Our - Orange

4 - Young - Yellow

5 - Guts - Green

6 - But - Black

7 - Vodka - Violet

8 - Goes - Grey

9 - Well - White