In a parallel circuit, how is the total resistance calculated?

• A. R_total = R1 + R2
• B. R_total = R1 × R2
• C. 1/R_total = 1/R1 + 1/R2 + ...
• D. R_total = 1 / (R1 + R2)

Answer: (C)

In a parallel circuit, resistors share the same voltage, and currents add through each path. The total resistance is found by adding the reciprocals of each branch’s resistance and then taking the reciprocal of that sum: 1/R_total = 1/R1 + 1/R2 + ... This shows why the total resistance is always less than any individual resistor—adding another path for current lowers the overall resistance. For two resistors, you can also write R_total = (R1 × R2) / (R1 + R2). For example, with 6 Ω and 3 Ω in parallel, 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R_total = 2 Ω. The other forms don’t describe parallel behavior: R_total = R1 + R2 is for series, R_total = R1 × R2 isn’t correct for parallel, and R_total = 1/(R1 + R2) misapplies the reciprocal.