#
Resistor Combinations

### 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** / **R**_{eff}.
In the original circuit,
**I** = **I**_{1} + **I**_{2},
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**/**R**_{1}) + (**V**/**R**_{2}).
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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Comments, suggestions, or requests to ghw@udel.edu.
"http://www.physics.udel.edu/~watson/scen103/circ2a.html"

Last updated Jan. 7, 1998.

Copyright George Watson, Univ. of Delaware, 1996.