[Syllabus logo] Resistor Combinations

Discussion of Parallel Combinations

[Schematic of parallel combination]

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.

[Schematic of equivalent circuit]

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.

[Schematics of equivalent circuits]

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:

[Formula for parallel resistance]

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.

Last updated Jan. 7, 1998.
Copyright George Watson, Univ. of Delaware, 1996.