# Definition of Equivalent Resistance [duplicate]

Is the equivalent resistance of two parallel resistors the resistance of the individual resistors or the sum of their resistances?

Is the $R_e$ of two series resistors their sum?

## marked as duplicate by Olin Lathrop, ACuriousMind♦, Kyle Kanos, Brandon Enright, BMSOct 28 '14 at 5:50

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## 2 Answers

The equivalent resistance of a network is that single resistor that could replace the entire network in such a way that for a certain applied voltage V you get the same current I as you were getting for a network.

If your network is "a bunch of resistors in a box", and you can't look inside the box (you just have access to the two terminals sticking out), then equivalent resistance is the simplest network you could imagine being in the box after doing some measurements on it.

The two simplest networks are two resistors in series (add their resistances to get the equivalent) or in parallel (then $R_e=\frac{R_1R_2}{R_1+R_2}$). But more complex combinations are possible - and while there may not be a "simple" formula to compute their equivalent resistance, a network with just two terminals always has an equivalent impedance.

The resistance of two parallel resistors is defined by:

$1/R_e = \sum1/R_i$

For two series resistors, it's simply the sum of the individual resistances of each resistor.