In an electronic filter circuit, two inductors with values L_1 = 30\text{ mH} and L_2 = 20… — Armed Services Vocational Aptitude Battery (ASVAB)

In an electronic filter circuit, two inductors with values $L_1 = 30\text{ mH}$ and $L_2 = 20\text{ mH}$ are connected in parallel. This parallel pair is connected in series with a third inductor $L_3 = 18\text{ mH}$ and a fourth inductor $L_4 = 10\text{ mH}$ . Assuming negligible mutual inductance between the coils, what is the total equivalent inductance of the circuit in millihenries ( $\text{mH}$ )?

Answer: 40 mH

Answer

40 mH

The total inductance is

40\text{ mH}

. Inductors follow the same combination rules as resistors: the parallel pair (

30\text{ mH}

and

20\text{ mH}

) yields an equivalent inductance of

12\text{ mH}

, which when added to the series inductors (

18\text{ mH}

and

10\text{ mH}

) gives

12 + 18 + 10 = 40\text{ mH}

Step-by-Step Solution

Calculate the equivalent inductance of the two parallel inductors

L_1

and

L_2

L_p = \frac{L_1 \times L_2}{L_1 + L_2} = \frac{30\text{ mH} \times 20\text{ mH}}{30\text{ mH} + 20\text{ mH}} = \frac{600}{50} = 12\text{ mH}

Inductors in parallel combine using reciprocal addition, identically to resistors in parallel.

Calculate the total circuit inductance by summing the parallel combination with the remaining series inductors

L_3

and

L_4

L_{total} = L_p + L_3 + L_4 = 12\text{ mH} + 18\text{ mH} + 10\text{ mH} = 40\text{ mH}

Inductors in series combine via direct addition because the magnetic fields and induced voltages add along the common current path.

Key Concept

Inductors combine like resistors: series inductances add directly, while parallel inductances combine using reciprocal addition.

Estimated Time:1m 30s

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