Discussion of Parallel Combinations
In this circuit, 1.5 A of current flows in the battery. This is the
same current that would flow if a 2 ohm resistor were the only
resistor connected to the battery, as below.
The 2 ohm resistance in this equivalent circuit is called the
effective resistance of the combination in the original
circuit. As far as the battery is concerned, the 2 ohm resistance is
effectively identical to the actual parallel combination of the 6 ohm
and 3 ohm resistors -- both result in 1.5 A through the battery.
The current in the battery in the equivalent circuit is
I = V / Reff.
In the original circuit,
I = I1 + I2,
the sum of currents in the 2 resistors.
Since the voltage across each resistor is the same, application of Ohm's
law results in
I = (V/R1) + (V/R2).
By comparison of this equation for the current in the battery and that
for the equivalent circuit, we find that the effective resistance is
given by the following formula:
Resistors are in parallel if both ends of each resistor are
connected directly together; the voltage across each element in
parallel is necessarily the same. Although 2 resistors were
considered above, any number of resistors may be combined in parallel.
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Last updated Jan. 7, 1998.
Copyright George Watson, Univ. of Delaware, 1996.