In a two-resistor parallel network, the reciprocal of the total resistance equals the sum of the reciprocals of the individual resistances.

• A. Reciprocal of total equals sum of reciprocals
• B. Total equals sum of reciprocals
• C. Total equals reciprocal of sum of reciprocals
• D. Total equals sum of direct values

Answer: (A)

When resistors are in parallel, the ways for current to flow add up, which means the total conductance increases. Conductance is the reciprocal of resistance, so the total conductance is the sum of the individual conductances: G_total = G1 + G2, with G1 = 1/R1 and G2 = 1/R2. Since G_total = 1/R_total, you get 1/R_total = 1/R1 + 1/R2. This directly describes how parallel resistances combine.

You can rearrange to R_total = 1/(1/R1 + 1/R2), which for two resistors simplifies to (R1 R2)/(R1 + R2). The option that states the total equals the sum of the reciprocals would describe conductance rather than resistance, so it doesn’t match what we’re solving for.