Electrical Circuits
Parallel Resistance
Parallel branches share the same voltage, and their currents add. Because each branch provides another path for charge, the equivalent resistance is lower than the smallest branch resistance. Reciprocals add for any number of branches; for exactly two resistors the product divided by the sum gives the same result more quickly.
Parallel Resistance
1 ÷ R_total = 1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn
Variables and units
| Symbol | Quantity | Unit |
|---|---|---|
| R_total | Equivalent resistance | Ω |
| R1 … Rn | Individual parallel resistances | Ω |
Conditions of application
Resistances connected across the same two nodes. The reciprocal form works for any number of branches; the product-over-sum shortcut applies only to exactly two.
Worked example
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Equivalent resistance of parallel branches and the current in each branch.