What is the formula for the equivalent resistance of resistors in parallel?

What is the formula for the equivalent resistance of resistors in parallel?

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

Answer: (B)

When resistors are in parallel, the paths for current multiply, so the total conductance is the sum of the individual conductances. This gives the relationship 1/R_eq = 1/R1 + 1/R2. Solving for R_eq from that equation yields R_eq = (R1 R2) / (R1 + R2), which is the same result expressed as a single fraction. This approach—adding conductances in parallel—is why the explicit form 1/R_eq = 1/R1 + 1/R2 is the best representation for parallel resistors.

When resistors are in parallel, the paths for current multiply, so the total conductance is the sum of the individual conductances. This gives the relationship 1/R_eq = 1/R1 + 1/R2. Solving for R_eq from that equation yields R_eq = (R1 R2) / (R1 + R2), which is the same result expressed as a single fraction. This approach—adding conductances in parallel—is why the explicit form 1/R_eq = 1/R1 + 1/R2 is the best representation for parallel resistors.