What is the total inductance when 12 mH and 24 mH are connected in parallel?

To determine the total inductance when inductors are connected in parallel, you use the formula for the total inductance of parallel inductors, which is the reciprocal of the sum of the reciprocals of each individual inductance.

For two inductors, the formula can be expressed as follows:

1 / L_total = 1 / L1 + 1 / L2

In this case, L1 is 12 mH, and L2 is 24 mH.

Calculating the reciprocals gives:

1 / L_total = 1 / 12 + 1 / 24

Finding a common denominator (which is 24) allows us to rewrite the equation:

1 / L_total = 2 / 24 + 1 / 24

1 / L_total = 3 / 24

This simplifies to:

1 / L_total = 1 / 8

To find L_total, take the reciprocal of 1 / 8:

L_total = 8 mH

This means that when 12 mH and 24 mH inductors are connected in parallel, the total inductance is 8 mH. The option reflecting this correct calculation is the choice that states 8 mH