A method for finding total resistance of parallel resistors is calculating the product over the sum.

A method for finding total resistance of parallel resistors is calculating the product over the sum.

• A. Depends on number of resistors
• B. Requires equal resistances
• C. False
• D. True

Answer: (D)

In parallel, resistances combine through their conductances. The total resistance is found from 1/Rt = 1/R1 + 1/R2 + ... For the common case of exactly two resistors in parallel, this simplifies to Rt = (R1 × R2) / (R1 + R2), which is the product over the sum. So the statement is true for two resistors in parallel. If more than two resistors are in parallel, you can’t use just the product over the sum; you must add all the reciprocals and then take the reciprocal of that sum (1/Rt = 1/R1 + 1/R2 + 1/R3 + ...).

In parallel, resistances combine through their conductances. The total resistance is found from 1/Rt = 1/R1 + 1/R2 + ... For the common case of exactly two resistors in parallel, this simplifies to Rt = (R1 × R2) / (R1 + R2), which is the product over the sum. So the statement is true for two resistors in parallel. If more than two resistors are in parallel, you can’t use just the product over the sum; you must add all the reciprocals and then take the reciprocal of that sum (1/Rt = 1/R1 + 1/R2 + 1/R3 + ...).