AC Components and Circuits
Inductance

Section 1-5 Total Inductance

Inductors in Series and Parallel

The total inductance of series and parallel inductor circuits is found by using the same form of equations you've been using for series and parallel resistor circuits.

Inductors in Series

LT = L1 + L2 + L3

Inductors in  Parallel

 LT = 1 1 + 1 + 1 L1 L2 L3

Equations

Total Inductance of a Series Circuit

LT = L1 + L2 + L3 + ... + Ln

Total Inductance of a Parallel Circuit

 LT = 1 1 + 1 + 1 +  ... + 1 L1 L2 L3 Ln

Where

LT = Total inductance of the series circuit
L1, L2, L3, Ln = Inductance of all the individual resistors

The product-over-sum technique that is commonly used for pairs of parallel resistors works equally well for pairs of inductors.

 LT = L1L2 L1 + L2

The shorthand notation for this equation is also to the resistance counterpart:

LT = L1 || L2

Example

Problem

Use the product-over-sum equation to find the total inductance of a parallel circuit comprised of inductors of 12mH and 22mH.

Procedure

1. Cite the appropriate equation:

 LT = L1L2 L1 + L2

2. Substitute the given values and do the math

 LT = (12 x 10-3)(22 x 10-3) = 7.76 x 10-3 (12 x 10-3) + (22 x 10-3

Solution

LT = 7.6 mH

Examples

Endless Examples & Exercises

 Given the values for inductors in series or parallel circuits, calculate the total capacitance. Work these exercises until you are confident you have mastered the procedures. Note: The answers shown in these example often do not appear in normalized forms. For example, an answer appears as 1200mH when it should be 1.2H.

Combination Inductor Circuits

 Inductors in Series-Parallel CombinationLT = L1 + (L2 || L3) Inductors in Parallel-Series CombinationLT = L1 || (L2 + L3)

The procedures for calculating the total inductance of combination inductor circuits is identical to those for combination resistor circuits. So a few exercises should be sufficient for mastering this particular topic.

Endless Examples & Exercises

 Given the values of the inductors in a combination circuit, calculate the total inductance.Work these examples until you are certain you understand the procedures.