When more than two inductors of different inductances are connected in parallel, the total inductance is which of the following?

When more than two inductors of different inductances are connected in parallel, the total inductance is which of the following?

• A. Less than the inductance of the lowest rated inductor
• B. Equal to the largest inductance
• C. Equal to the sum of the inductances
• D. Greater than the smallest inductance

Answer: (A)

In a parallel connection, inductors share the same voltage, and their ability to oppose a change in current combines in such a way that the total inductance is smaller than any individual one. The relationship is 1/L_total = 1/L1 + 1/L2 + ... For positive inductances, this sum is always larger than 1 divided by the smallest inductance, so L_total is less than the smallest inductance in the group. For example, two inductors of 2 H and 3 H in parallel give L_total = 1/(1/2 + 1/3) = 1/(5/6) = 1.2 H, which is less than both 2 H and 3 H. So the total inductance in parallel is always less than the smallest inductance among the inductors involved. The other possibilities describe series behavior (the sum) or incorrect comparisons to the largest or smallest values.

In a parallel connection, inductors share the same voltage, and their ability to oppose a change in current combines in such a way that the total inductance is smaller than any individual one. The relationship is 1/L_total = 1/L1 + 1/L2 + ... For positive inductances, this sum is always larger than 1 divided by the smallest inductance, so L_total is less than the smallest inductance in the group.

For example, two inductors of 2 H and 3 H in parallel give L_total = 1/(1/2 + 1/3) = 1/(5/6) = 1.2 H, which is less than both 2 H and 3 H.

So the total inductance in parallel is always less than the smallest inductance among the inductors involved. The other possibilities describe series behavior (the sum) or incorrect comparisons to the largest or smallest values.