Series and Parallel Circuits

Contributors: Pete-O
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Calculating Equivalent Resistances in Parallel Circuits

What about parallel resistors? That’s a bit more complicated, but not by much. Consider the last example where we started with a 10V supply and a 10kΩ resistor, but this time we add another 10kΩ in parallel instead of series. Now there are two paths for current to take. Since the supply voltage didn’t change, Ohm’s Law says the first resistor is still going to draw 1mA. But, so is the second resistor, and we now have a total of 2mA coming from the supply, doubling the original 1mA. This implies that we’ve cut the total resistance in half.

Schematic: Two parallel resistors in parallel with a battery

While we can say that 10kΩ || 10kΩ = 5kΩ (“||” roughly translates to “in parallel with”), we’re not always going to have 2 identical resistors. What then?

The equation for adding an arbitrary number of resistors in parallel is:

1/Rtot = 1/R1 + 1/R2 + ... + 1/R(N-1) + 1/RN

If reciprocals aren’t your thing, we can also use a method called “product over sum” when we have two resistors in parallel:

R1||R2 = R1*R2/(R1+R2)

However, this method is only good for two resistors in one calculation. We can combine more than 2 resistors with this method by taking the result of R1 || R2 and calculating that value in parallel with a third resistor (again as product over sum), but the reciprocal method may be less work.