Figuring total resistance for resistors in parallel is a chore confronted by early students of electronics. The general method that works for any situation is to take the reciprocal of each resistance, add these together, and take the reciprocal of the result. A couple of tricks can cut this task down to size. If all the resistors have the same value, divide the resistance of one resistor by the number of resistors. If you’re finding the value of two resistors in parallel, divide the product of their resistances by their sum.
General Case
Take the reciprocal of each resistance. Example: For three resistors in parallel, 15, 20 and 25 ohms. The reciprocals are 1/15, 1/20 and 1/25.
Add the reciprocals together. Example: 1/15 + 1/20 + 1/25 = .157
Take the reciprocal of the result. This gives the total resistance of the parallel combination. Example: 1/.157 = 6.4 ohms
All the Same Value
Determine the resistance. Example: Three resistors in parallel, all 300 ohms. The resistance to divide is 300 ohms.
Count the resistors. Example: 3
Divide the resistance by the count. This give the total resistance. Example: 300/3 = 100 ohms.
Pair of Resistors
Multiply the resistances. Example: Two resistors in parallel, 100 and 200 ohms. 100 x 200 = 20,000
Add the resistances. Example: 100 + 200 = 300
Divide the result in Step 1 by the result in Step 2. This gives you the total resistance. Example: 20,000 / 300 = 66.7 ohms.
About the Author
Chicago native John Papiewski has a physics degree and has been writing since 1991. He has contributed to "Foresight Update," a nanotechnology newsletter from the Foresight Institute. He also contributed to the book, "Nanotechnology: Molecular Speculations on Global Abundance." Please, no workplace calls/emails!
Photo Credits
Comstock/Comstock/Getty Images