Gas station without pumps

2014 April 18

Voltage dividers, parallel impedance, scope probes

Filed under: Circuits course — gasstationwithoutpumps @ 20:26
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I started today’s class by having the students present what they had done on the homework I assigned at the end of class Wednesday.  The first part was a voltage divider with one resistor above the output and two in series below the output. Everyone got this, either by direct reasoning about the currents matching or by using the two-resistor voltage divider formula and that two resistors in series add.  The next problem was a little harder:

You have sensor whose resistance varies from 1kΩ to 4kΩ with the property it measures and a 5v power supply.  Design a circuit whose output voltage varies from 1v (at 1kΩ) to 2v (at 4kΩ).

For this one we first had two non-solutions presented. One student tried using a simple voltage divider, and found the resistance for which some power supply would produce the desired outputs, but (unfortunately) the necessary power supply was not 5v. one student showed a use for the 3-resistor voltage divider, but got the values of the resistors wrong, so that a simple sanity check showed that the answer didn’t work. Another student came up with a circuit that “cheated” by assuming 2 more power supplies (at 1v and 2v). If he had known how to create such virtual power supplies, I would have given him credit, but he had no idea how to create them from the 5v supply. While that was being presented the student with the 3-resistor voltage divider, redid his arithmetic and got results that were almost ok (a percent or two off), so I had him present his method. The method set up the right equations, but his method for solving them was a bit messier and more complex than needed, so I showed the students how to set up the voltage divider equation as the inverse of current (R/V) being identical, and then solving the simple linear equations that resulted.

We next derived the formula for parallel resistances R= \frac{1}{\frac{1}{R_{1}}+\frac{1}{R_{2}}+\;\cdots\;+\frac{1}{R_{n}}}, using just Ohm’s Law and Kirchhoff’s  current law. I explained the concept of conductance, and gave them the rule of thumb: resistances add in series, conductances add in parallel.

I then talked a bit about scope probes and worked up to the following circuit:

Approximate circuit for my cheap 60MHz scope probes.

Approximate circuit for my cheap 60MHz scope probes.

Monday I’ll have to talk a little about electrodes and electrochemistry, but I also want students to do another voltage divider exercise in class—perhaps an RC one. Wednesday will be analysis of the data from the stainless-steel electrodes, and Friday will be a simple voltage divider and complex impedance quiz.

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