Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

An arbitrary number of identical resistors in parallel

Uniting four resistors in parallel is equivalent to making a single resistor with the same length but four times the cross-sectional area. The result is to make a resistor with one quarter the resistance.

Question: What is the resistance of N identical resistors in parallel?

Solution: Generalizing the results for two and three resistors, we have

where "..." means that the sum includes all the resistors. If all the resistors are identical, this becomes

Last Update: 2009-06-21