During this semester, which mostly consists of electricity and magnetism, I’ve really started to appreciate that the content is the vehicle through which students develop problem solving, critical thinking, and long-chains of reasoning. Later I will write how electrostatics is a great start to developing these long-chains of reasoning before we really exercise that skill with circuits. While not as challenging, circuit analysis is a good application of problem solving skills that illustrates how organizing data can make it much easier to solve problems.
We’ve started calling this problem-solving approach Circuit Sodoku.
The technique has evolved over the years based on input by teachers and students. I expect that it is similar to techniques used elsewhere. Regardless, my students find it very helpful when analyzing complex circuits.
At the heart of the technique is the V = IR table which has the following elements described below and illustrated in the photo of a group’s whiteboard: * three columns: V (voltage), I (current), and R (resistance) * the first row represents the equivalent circuit which specifies the voltage of the source, the current through the source, and the equivalent resistance of the circuit. * each subsequent row corresponds to a resistor in the circuit
Students follow these steps to analyze circuits: 1. solve for the equivalent resistance (redrawing the circuit after each step, if necessary) 2. calculate the current through the supply based on the supply’s voltage and equivalent resistance 3. look for resistors in series or parallel with the source and update the table with the current or voltage associated with that resistor 4. apply the loop rule and junction rule to complete blanks in the table
Whenever two of the three columns for a row are completed, students use Ohm’s Law to calculate the third value.
Here’s an example:
Just to be clear, Circuit Sodoku is not the heart of our circuits unit. Before we start analyzing circuits in this manner, we have spent weeks developing our conceptual understanding of circuits using the CASTLE curriculum. Many students find Circuit Sodoku a welcome break at the end of the unit.
Circuit Sodoku used to be the most challenging problem-solving application of my circuit unit. Now it is the easiest. I’m pleased we are focusing more on developing these essential problem solving, critical thinking, and long-chains of reasoning skills.