For N identical resistors in parallel, the total resistance is R divided by N.

• A. equal to R
• B. equal to R/N
• C. equal to R × N
• D. equal to N/R

Answer: (B)

In parallel, the total resistance comes from adding the conductances (the reciprocals of resistance) of each path. The relationship is 1/R_eq = 1/R1 + 1/R2 + ... + 1/RN. If all resistors have the same value R, this becomes 1/R_eq = N/R, so R_eq = R/N. This shows why adding more identical resistors in parallel reduces the total resistance, since you’re effectively spreading the current over more paths. The result matches the statement that the total resistance is R divided by N. The other possibilities would correspond to different arrangements: R would be the value for a single path, R*N would be the series combination, and N/R is the reciprocal of the total resistance, not the resistance itself.