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How is the total resistance of resistors in parallel calculated?

by in Electrical Engineering 112 views
How is the total resistance of resistors in parallel calculated?

1 Answer

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The total resistance of resistors in parallel is calculated using the following formula:

1 / R_total = 1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn

where:
R_total is the total resistance of the parallel combination,
R1, R2, R3, ... Rn are the individual resistances of each resistor in parallel.

In words, to find the reciprocal of the total resistance, you add the reciprocals of the individual resistances, and then take the reciprocal of the sum.

Once you have the value of R_total (the total resistance reciprocal), you can find the total resistance (R_total) by taking the reciprocal of the total resistance reciprocal:

R_total = 1 / (1 / R1 + 1 / R2 + 1 / R3 + ... + 1 / Rn)

When two resistors are in parallel, the total resistance is always less than the smallest resistance in the group. As you add more resistors in parallel, the total resistance will decrease further. This is because in a parallel configuration, each resistor provides an additional path for current to flow, reducing the overall resistance in the circuit.
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