[Syllabus logo] Resistor Combinations

Discussion of Series Combinations

[Schematics of equivalent circuits]

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:

[Formula for series resistance]

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.