Name: equivalent inductance in circuit networks
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Series and Parallel Inductors

Inductors connected in series and/or parallel configurations can be simplified to an equivalent single inductor.
Consider a series connection of inductors with the same current flowing through them.
When Kirchhoff&#39;s voltage law is applied to the loop, and the expression for the inductor voltages is substituted, the resulting expression indicates that the equivalent inductance of these series-connected inductors equals the sum of the individual inductances.
Next, consider a parallel connection of inductors, where each inductor experiences the same voltage across it. Kirchhoff&#39;s current law is applied to the loop, and the expression for the inductor current is substituted.
Since the initial current through the equivalent inductor is the sum of the individual inductor currents, the sum of the reciprocals of the individual inductances equals the reciprocal of the equivalent inductance.
Inductor combinations in series and in parallel follow similar rules as resistors.
Consider a circuit with both series and parallel inductors. The equivalent inductance of the parallel combination of inductors is calculated and added to the series inductance to obtain the total equivalent inductance.

series and parallel inductors

In electrical circuits, integrating inductors into the toolkit of passive elements requires navigating the intricacies of series and parallel combinations involving these components. Practical circuits often feature configurations of multiple inductors, and understanding how to determine their equivalent inductance is vital.
For a series connection of N inductors, each carrying the same current, applying Kirchhoff's voltage law unveils a crucial relationship. Substituting the expression for inductor voltages leads to an insightful conclusion: the equivalent inductance of this series arrangement is the simple summation of the individual inductances. This phenomenon mirrors how resistors combine in series, emphasizing a fundamental similarity between these passive elements.
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In a parallel connection of inductors, each bears an identical voltage; Kirchhoff's current law can be applied. This leads to a significant revelation: the reciprocal of the equivalent inductance is equal to the sum of the reciprocals of the individual inductances. This parallel combination rule mirrors the behavior of resistors in parallel, illustrating a harmonious approach to dealing with different passive elements.
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In practice, circuits often feature a blend of series and parallel inductors. When confronted with such scenarios, the equivalent inductance of the parallel inductors is calculated and added to the series inductance to obtain the overall equivalent inductance of the circuit.

Inductors connected in series and/or parallel configurations can be simplified to an equivalent single inductor.
Consider a series connection of inductors ...

Education

JoVE Core

Electrical Engineering

Unit 1

Energy Storage Elements

KEY TERMS AND CONCEPTS

equivalent inductance in circuit networks

Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage.

For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is the same pattern used for resistors in series.

For inductors in parallel, each branch has the same voltage. Kirchhoff's current law gives the key relationship for this arrangement. The reciprocal of the equivalent inductance equals the sum of the reciprocals of the individual inductances. This matches the rule used for resistors in parallel.

Many practical circuits use a mix of series and parallel inductors. In those cases, the parallel inductors are first combined into one equivalent inductance. That result is then added to the inductance in series to find the total equivalent inductance of the circuit.

Equivalent Inductance in Circuit Networks

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Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage. For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is...

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Learn how series and parallel inductors combine in circuits. See how Kirchhoff's laws give the rules for equivalent inductance in mixed networks.

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Equivalent Inductance in Circuit Networks

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