Which formula correctly gives the total resistance of two resistors in parallel?

• A. 1/R_total = 1/R1 + 1/R2
• B. R_total = R1 + R2
• C. R_total = R1 × R2
• D. V = I × R

Answer: (A)

When resistors are connected in parallel, the same voltage is across each resistor and the total current is the sum of the branch currents. Since each current is I = V/R, the total current is I_total = V/R1 + V/R2 = V(1/R1 + 1/R2). Using Ohm’s law for the whole network, the total resistance is R_total = V/I_total = 1/(1/R1 + 1/R2). This is why the reciprocal form correctly gives the total resistance in parallel.

For a quick check, if R1 = 4 Ω and R2 = 6 Ω, 1/R_total = 1/4 + 1/6 = 5/12, so R_total = 12/5 = 2.4 Ω, which is less than either resistor.

Adding resistances (R_total = R1 + R2) applies to series connections, not parallel. The product R1 × R2 isn’t a general formula for parallel resistance, and V = I × R is Ohm’s law, not a direct formula for total resistance in a network.