How do you calculate total resistance in a parallel circuit?

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

Answer: (D)

In parallel, all components experience the same voltage and the total current is the sum of the currents through each branch. Each branch draws current equal to V divided by its resistance, so the total current is V times the sum of the reciprocals of the branch resistances. Using Ohm’s law, R_total = V / I_total becomes R_total = 1 / (1/R1 + 1/R2 + 1/R3 + …). This is the essence of calculating total resistance in parallel: you invert the sum of the reciprocals of the individual resistances.

If you want a quick sense of the numbers, plug in some values: with 4 Ω, 6 Ω, and 12 Ω in parallel, 1/R_total = 1/4 + 1/6 + 1/12 = 0.5, so R_total = 2 Ω.

The other forms don’t reflect parallel behavior: adding resistances directly is for series, and combining in a way like (R1 × R2)/(R1 + R2) + R3 would correspond to two in parallel (then in series with the third) rather than all three in parallel.