How do you find the total resistance in a parallel circuit?

• A. Rtotal = R1 + R2 + R3 + ...
• B. 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ...
• C. Rtotal = (R1 * R2) / (R1 + R2)
• D. Rtotal = R1 * R2 * R3

Answer: (B)

The formula for finding the total resistance in a parallel circuit is based on the principle that the reciprocal of the total resistance is equal to the sum of the reciprocals of the individual resistances. This is represented as 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ..., which allows you to account for how current divides among the branches of the circuit.

In parallel circuits, the voltage across each component is the same, and as a result, the currents through each resistor can be added together. The more resistors you add in parallel, the lower the total resistance becomes because additional paths are available for current to flow. Since the relationship is expressed in terms of reciprocals, the correct formula ensures that as more resistors are added, 1/Rtotal decreases, leading to a lower overall resistance.

Using this formula, if you have two resistors in parallel, for example, you can easily calculate the total resistance by taking the reciprocal of the sum of the reciprocals of the individual resistances. This method accurately reflects how current interacts in parallel configurations, making it the definitive approach for determining total resistance in these circuits.