Three resistors in parallel: 10 ohm, 20 ohm, 20 ohm. What is the total resistance?

Three resistors in parallel: 10 ohm, 20 ohm, 20 ohm. What is the total resistance?

• A. 6
• B. 10
• C. 4
• D. 5

Answer: (D)

In parallel, the total resistance comes from adding the conductances (the reciprocals of the resistances) and then taking the reciprocal of that sum. So calculate 1 over the total resistance equals 1/10 plus 1/20 plus 1/20. That’s 0.1 + 0.05 + 0.05 = 0.2. The total resistance is the reciprocal of 0.2, which is 5 ohms. This fits the rule that the equivalent resistance in parallel is always less than the smallest individual resistance, here 5 is less than 10. The other numbers would come from incorrect arithmetic or applying a different arrangement; they don’t match the correct sum of reciprocals.

In parallel, the total resistance comes from adding the conductances (the reciprocals of the resistances) and then taking the reciprocal of that sum. So calculate 1 over the total resistance equals 1/10 plus 1/20 plus 1/20. That’s 0.1 + 0.05 + 0.05 = 0.2. The total resistance is the reciprocal of 0.2, which is 5 ohms. This fits the rule that the equivalent resistance in parallel is always less than the smallest individual resistance, here 5 is less than 10. The other numbers would come from incorrect arithmetic or applying a different arrangement; they don’t match the correct sum of reciprocals.