Which expression correctly shows the total resistance for a three-branch parallel circuit?

• A. R_total = R1 + R2 + R3
• B. R_total equals R1 parallel R2 parallel R3
• C. 1/R_total = 1/R1 + 1/R2 + 1/R3
• D. R_total equals the smallest branch resistance

Answer: (C)

In a parallel circuit, each branch provides its own path for current, but all branches share the same voltage. Because currents add while the voltage stays the same, the total resistance is found by summing the reciprocals of each branch’s resistance. This gives 1/R_total = 1/R1 + 1/R2 + 1/R3. Taking the reciprocal of that sum yields the total resistance for the three parallel paths.

This expression correctly captures how adding more parallel paths lowers the overall resistance. For example, if all three branches have the same resistance R, then 1/R_total = 3/R, so R_total = R/3, clearly demonstrating the reduction.

The other ways described don’t match how parallel resistance behaves: summing the resistances is for series connections; saying the total is simply the smallest branch is false because the total is always less than the smallest individual resistance when positive resistances are present; and a statement like “R_total equals R1 parallel R2 parallel R3” isn’t a concrete form to compute a value.