If you double the number of identical resistors in parallel, what happens to the total resistance?

• A. The total resistance doubles.
• B. The total resistance halves.
• C. The total resistance remains the same.
• D. The total resistance increases by the square root of two.

Answer: (B)

In parallel, adding more identical resistors increases the number of paths for current, so the overall resistance drops. For n identical resistors each with resistance R, the combined resistance is R/n. If you double the number of resistors in parallel (to 2n), the total resistance becomes R/(2n), which is half of the original R/n. This happens because the total conductance adds: conductance = n/R, so resistance = 1/(n/R) = R/n; doubling n doubles the conductance and halves the resistance.