If all resistors in parallel have the same value, then the total resistance is equal to the value of any one resistor divided by the total number of resistors.

If all resistors in parallel have the same value, then the total resistance is equal to the value of any one resistor divided by the total number of resistors.

• A. equal to
• B. equal to R/N
• C. the product of
• D. the reciprocal of

Answer: (B)

When resistors are in parallel, the total resistance is found from the reciprocal rule: 1 over the total resistance equals the sum of the reciprocals of each individual resistance. If all N resistors have the same value R, then each reciprocal is 1/R, and adding them gives 1/R_total = N*(1/R) = N/R. Invert to get R_total = R/N. So the total resistance is indeed the value of a single resistor divided by the number of resistors in parallel. This isn’t equal to the value of one resistor, since adding parallel paths lowers the total resistance. It isn’t the product of resistances, and it isn’t simply the reciprocal of a single resistor value in this setup.

When resistors are in parallel, the total resistance is found from the reciprocal rule: 1 over the total resistance equals the sum of the reciprocals of each individual resistance. If all N resistors have the same value R, then each reciprocal is 1/R, and adding them gives 1/R_total = N*(1/R) = N/R. Invert to get R_total = R/N. So the total resistance is indeed the value of a single resistor divided by the number of resistors in parallel.

This isn’t equal to the value of one resistor, since adding parallel paths lowers the total resistance. It isn’t the product of resistances, and it isn’t simply the reciprocal of a single resistor value in this setup.