For parallel circuits with three resistors, which expression gives the reciprocal of the total resistance?

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

Answer: (B)

In parallel circuits, the currents have multiple paths and the conductances add up. The total conductance is the sum of the conductances of each resistor, and the reciprocal of the total resistance equals this total conductance. So the correct relationship is that the reciprocal of the total resistance equals the sum of the reciprocals of each resistor: 1/Rt = 1/R1 + 1/R2 + 1/R3. This aligns with voltage being the same across all resistors and currents adding: I = V/R1 + V/R2 + V/R3, and since Rt = V/I, you get 1/Rt = I/V = 1/R1 + 1/R2 + 1/R3. The other forms correspond to different things: adding the resistances gives the series case, and using only two reciprocals or taking the reciprocal of a sum wouldn’t accurately reflect three parallel paths.