How is the total resistance calculated for resistors connected in parallel?

• A. Rtotal = R1 + R2 + ...
• B. sqrt(R1^2 + R2^2)
• C. 1/Rtotal = 1/R1 + 1/R2 + ...
• D. Rtotal = R1 / R2

Answer: (C)

When resistors are in parallel, the voltage across each one is the same, and the total current is the sum of the currents through each path. Using Ohm’s law for each resistor, I = V/R, the total current is I_total = V/R1 + V/R2 + ... = V(1/R1 + 1/R2 + ...). The total resistance is defined by I_total = V/Rtotal, so V/Rtotal = V(1/R1 + 1/R2 + ...). Cancel V to get 1/Rtotal = 1/R1 + 1/R2 + ..., which is the rule for combining resistors in parallel. A practical takeaway is that conductances add: G = 1/R, so G_total = G1 + G2 + ... . For two resistors, you can also use Rtotal = (R1*R2)/(R1+R2). For example, two 6-ohm resistors in parallel give Rtotal = 3 ohms. The other forms—adding in series (Rtotal = R1 + R2), using a square root, or taking a ratio like R1/R2—do not reflect how parallel networks share voltage and currents.