For two resistors in parallel, which expression correctly represents the total resistance?

For two resistors in parallel, which expression correctly represents the total resistance?

• A. Rt = R1 + R2
• B. Rt = (R1 R2) / (R1 + R2)
• C. 1/Rt = 1/R1 + 1/R2
• D. 1/Rt = 1/R1 - 1/R2

Answer: (C)

In a parallel circuit, the total resistance is found by adding the reciprocals of each resistor’s resistance and then taking the reciprocal of that sum. This reflects how current can split between the paths, effectively adding the conductances (the reciprocals of resistance). So the direct relation is 1/Rt = 1/R1 + 1/R2. If you solve for Rt, you get Rt = (R1 R2) / (R1 + R2), which is another correct way to express the same idea. The other idea, Rt = R1 + R2, would apply when the resistors are in series, not parallel. The expression 1/Rt = 1/R1 - 1/R2 is not correct for parallel resistance because you don’t subtract the reciprocals in this configuration.

In a parallel circuit, the total resistance is found by adding the reciprocals of each resistor’s resistance and then taking the reciprocal of that sum. This reflects how current can split between the paths, effectively adding the conductances (the reciprocals of resistance).

So the direct relation is 1/Rt = 1/R1 + 1/R2. If you solve for Rt, you get Rt = (R1 R2) / (R1 + R2), which is another correct way to express the same idea.

The other idea, Rt = R1 + R2, would apply when the resistors are in series, not parallel. The expression 1/Rt = 1/R1 - 1/R2 is not correct for parallel resistance because you don’t subtract the reciprocals in this configuration.