Understanding Inductors in Series

When inductors are connected in series, the total inductance is the sum of the individual inductances, provided there is no mutual inductance between them.

Formula:

\( L_{\text{total}} = L_1 + L_2 + \ldots + L_n \)

The total inductance of a series configuration is always greater than the largest individual inductance in the group.

Key Points to Remember:

• The total inductance in a series connection increases with each added inductor.
• All inductors in series share the same current, but their voltage drops differ depending on their inductance values.
• Series inductors are commonly used to achieve a desired inductance value that may not be available as a single component.

Example Calculations

Example 1:

Given: \( L_1 = 10 \, \text{mH}, L_2 = 20 \, \text{mH}, L_3 = 30 \, \text{mH} \)

Calculation:

1. Convert all inductances to Henries: \[ L_1 = 0.01 \, \text{H}, \, L_2 = 0.02 \, \text{H}, \, L_3 = 0.03 \, \text{H} \]
2. Apply the formula: \[ L_{\text{total}} = L_1 + L_2 + L_3 = 0.01 + 0.02 + 0.03 = 0.06 \, \text{H} \]
3. Convert back to millihenries: \[ L_{\text{total}} = 0.06 \times 1000 = 60 \, \text{mH} \]

Result: \( L_{\text{total}} = 60 \, \text{mH} \)

Example 2:

Given: \( L_1 = 50 \, \mu\text{H}, L_2 = 100 \, \mu\text{H} \)

Calculation:

1. Convert all inductances to Henries: \[ L_1 = 50 \times 10^{-6} \, \text{H}, \, L_2 = 100 \times 10^{-6} \, \text{H} \]
2. Apply the formula: \[ L_{\text{total}} = L_1 + L_2 = 50 \times 10^{-6} + 100 \times 10^{-6} = 150 \times 10^{-6} \, \text{H} \]
3. Convert back to microhenries: \[ L_{\text{total}} = 150 \, \mu\text{H} \]

Result: \( L_{\text{total}} = 150 \, \mu\text{H} \)