For two resistors in parallel, which equation correctly expresses the relationship for the total resistance Rt?

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

Answer: (D)

In parallel, resistances combine through a reciprocal sum, so the total resistance is smaller than either resistor. The relationship is that the reciprocal of the total resistance equals the sum of the reciprocals of each individual resistance. This is the best expression because it matches how current splits between the branches and how resistance adds in the inverse way.

If you work with numbers, for example R1 = 4 Ω and R2 = 6 Ω, you get 1/Rt = 1/4 + 1/6 = 5/12, so Rt = 12/5 = 2.4 Ω. This shows Rt is indeed less than both 4 Ω and 6 Ω, as expected for parallel paths. You can also rearrange to Rt = (R1*R2)/(R1 + R2) if you prefer an explicit Rt formula.

The other forms don’t fit: adding the resistances is for a series configuration; Rt = R1 // R2 isn’t a standard algebraic expression for a total resistance; and Rt = 1/R1 + 1/R2 would give a sum of reciprocals without taking the reciprocal to obtain Rt itself.