Discussion of Series Combinations
The same current is required to flow in the original circuit and the
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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Last updated Sept. 17, 1996.
Copyright George Watson, Univ. of Delaware, 1996.