4.7:
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'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'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.
4.7:
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.
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.
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.