In a parallel circuit, the total resistance equals the reciprocal of the sum of the reciprocals of the individual resistances. Which option correctly expresses this statement?

• A. It is greater than the largest resistance.
• B. It is equal to the sum of all resistances.
• C. It is less than the smallest resistance.
• D. It equals the reciprocal of the sum of the reciprocals of the resistances.

Answer: (D)

In a parallel circuit, the total resistance is found by adding up the reciprocals of each individual resistance to get the total conductance, and then taking the reciprocal of that sum to get the total resistance. In formula form, R_total = 1 / (1/R1 + 1/R2 + ...). This is exactly what the statement expresses.

For example, if you have two resistors of 4 ohms and 6 ohms in parallel, 1/R_total = 1/4 + 1/6 = 0.4167, so R_total ≈ 2.4 ohms. This shows why the total resistance is smaller than either resistor in parallel.

The other options describe related ideas but do not state the specific reciprocal-of-sum formula. It’s true that the total resistance in parallel is less than the smallest individual resistance, and that it’s not simply the sum of resistances (that would be a series case), but the exact expression asked for is the reciprocal of the sum of the reciprocals.