# Resistor Combinations

### Discussion of Series Combinations

The same current is required to flow in the original circuit and the equivalent circuit. The voltage across the resistor in the equivalent circuit is given by Ohm's law V = I Reff. In the original circuit, the voltage across the battery V = V1 + V2, the sum of the individual voltages across the resistors. Applying Ohm's law to each resistor, V = I R1 + I R2. By comparison of this equation for the voltage across the battery and that for the equivalent circuit, we find that the effective resistance is given by the following formula:

Resistors are in series if one end of each resistor is connected together, with no other circuit element connected at that point; the current through each element in series is necessarily the same. Although 2 resistors were considered above, any number of resistors may be combined in series.

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"http://www.physics.udel.edu/~watson/scen103/circ3a.html"
Last updated Sept. 17, 1996.
Copyright George Watson, Univ. of Delaware, 1996.