Equation 1: Req = 1/(1/R1 + 1/R2 + 1/R3 + ..... + 1/Rn)
For the circuit shown below, where R1 = 2 Ohms, R2 = 4 Ohms and R3 = 4 Ohms, the equivalent resistance calculated with equation 1 is
Req = 1/(1/R1 + 1/R2 + 1/R3)
Req = 1/(1/2 + 1/4 + 1/4) = 1/(6/12 + 3/12 + 3/12) = 1/(12/12) = 1 Ohm
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| The equivalent resistance of resistors in parallel is always lower than the lowest value resistor |
Circuit Applications
Resistors are often placed in parallel to construct a resistor that doesn't come in a standard value or, in many cases, to allow the use of resistors with lower power ratings. When resistors are placed in parallel the current splits between the different branches in the parallel circuit. The amount of current in each branch is proportional to the resistance in each branch. Branches with lower resistance will conduct more current.
Another reason to place resistors in parallel is even heat distribution. Current flow results in energy dissipation which in turn results in heat. If one resistor is used instead of several resistors in parallel the heat will be more concentrated on the circuit board. As well, the large resistor will need a higher power rating. The higher levels of concentrated heat may result in a design that has a lower mean time between failure. This can be especially true in designs that must carry a significant amount of current.
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