In a two-resistor parallel circuit, total resistance is described as:

In a two-resistor parallel circuit, total resistance is described as:

• A. The sum of the resistances
• B. The reciprocal of the sum of the reciprocals
• C. The quotient of the larger resistance by the smaller
• D. The difference of the resistances

Answer: (B)

When resistors are in parallel, the same voltage drives each branch, and the total current is the sum of the branch currents. The current through each resistor is V/R1 and V/R2, so I_total = V(1/R1 + 1/R2). Using Ohm’s law for the combined circuit, R_total = V/I_total = 1 / (1/R1 + 1/R2). That is exactly the idea of the reciprocal of the sum of the reciprocals. This can also be written as R_total = (R1 × R2) / (R1 + R2), and it will always be less than either individual resistance.

When resistors are in parallel, the same voltage drives each branch, and the total current is the sum of the branch currents. The current through each resistor is V/R1 and V/R2, so I_total = V(1/R1 + 1/R2). Using Ohm’s law for the combined circuit, R_total = V/I_total = 1 / (1/R1 + 1/R2). That is exactly the idea of the reciprocal of the sum of the reciprocals. This can also be written as R_total = (R1 × R2) / (R1 + R2), and it will always be less than either individual resistance.