In a parallel circuit, the reciprocal of total resistance equals the sum of reciprocals of the individual resistances.

In a parallel circuit, the reciprocal of total resistance equals the sum of reciprocals of the individual resistances.

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

Answer: (A)

In a parallel circuit, adding more paths for current lowers the overall resistance, and the relationship is captured by taking reciprocal values. The total resistance is found by taking the reciprocal of the sum of the reciprocals of each individual resistance: 1/Rt = 1/R1 + 1/R2 + 1/R3. This form works for any number of resistors in parallel and shows why Rt becomes smaller as more branches are added. This is the best choice because it directly matches how parallel resistances combine: each branch contributes its conductance (the reciprocal of resistance) to the total conductance. If you had only two resistors, you could also write Rt = (R1 R2)/(R1+R2), but that specific two-resistor form doesn’t extend to three or more without the reciprocal-sum expression. The other options describe series behavior, include an unnecessary minus sign, or give the two-resistor parallel result in a way that doesn’t account for the third resistor.

In a parallel circuit, adding more paths for current lowers the overall resistance, and the relationship is captured by taking reciprocal values. The total resistance is found by taking the reciprocal of the sum of the reciprocals of each individual resistance: 1/Rt = 1/R1 + 1/R2 + 1/R3. This form works for any number of resistors in parallel and shows why Rt becomes smaller as more branches are added.

This is the best choice because it directly matches how parallel resistances combine: each branch contributes its conductance (the reciprocal of resistance) to the total conductance. If you had only two resistors, you could also write Rt = (R1 R2)/(R1+R2), but that specific two-resistor form doesn’t extend to three or more without the reciprocal-sum expression. The other options describe series behavior, include an unnecessary minus sign, or give the two-resistor parallel result in a way that doesn’t account for the third resistor.