Two identical resistors in parallel are connected to a voltage source. The equivalent resistance is?

• A. R
• B. R/2
• C. 2R
• D. R/3

Answer: (B)

When resistors are in parallel, the voltage across each one is the same, and the total current is the sum of the individual currents. For two identical resistors R, each path carries I = V/R, so the total current is 2V/R. The equivalent resistance is V divided by that total current, giving R_eq = V / (2V/R) = R/2. Equivalently, 1/R_eq = 1/R + 1/R = 2/R, which again yields R_eq = R/2. The intuition is that adding another identical path doubles the circuit’s ability to carry current, so the effective resistance halves. It’s not R, because the parallel arrangement lowers resistance; it’s not 2R, which would be the series case; and it’s not R/3, which would require three parallel paths.