Sunday, September 6, 2009

Teaching Ohm's Law for Parallel Circuits

Many students have a hard time understanding why the total resistance of a parallel circuit decreases as loads are added in parallel. Comparing lanes on a highway to loads in a parallel circuit is an analogy that works for many people. Adding another load in a parallel circuit is like adding another lane on a highway. The more lanes you have, the more traffic you can move. So as lanes are added, the resistance to traffic flow decreases. In parallel circuits, the more loads you have in parallel, the more current you can move. So adding loads in parallel decreases resistance to current flow. The total resistance in a parallel circuit is difficult to calculate because it cannot simply be added as in a series circuit. However, the total current flow in a parallel circuit is easy to calculate. It is simply the sum of the currents for all the individual loads. The famous parallel formula for resistances in parallel uses this concept. Dividing the resistance of each load into 1 calculates the current draw for each load at 1 volt. Adding these fractions gives the total current draw of the entire circuit at 1 volt. Since resistance can be calculated by dividing current into voltage, dividing the total circuit current at 1 volt into 1 volt gives the total resistance. I confess that I have used and taught this formula for many years without knowing why it works. Once I understood the reason behind the formula, it seemed far more logical and less imposing.If you want to have some fun, take a parallel circuit calculation and use a number other than one, say 5. Divide each resistance into 5 to get the current for each load at 5 volts. Add all the individual currents up. Finally divide this total current into 5 to get the total resistance. You get the same answer as when you use 1! To prove it to yourself, do the same set of resistances with several voltages. If you don’t stumble on the math, the answer is always the same regardless of the number you start with.

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