Calculate the equivalent inductance Leq of two ideal inductors, L1 and L2, connected in series i

step 1 we have the change in equivalent current equals changing current in the first loop equals changi

Calculate the equivalent inductance Leq of two ideal...

Calculate the equivalent inductance $L_{\mathrm{eq}}$ of two ideal inductors, $L_{1}$ and $L_{2},$ connected in series in a circuit. Assume that their mutual inductance is negligible. [Hint: Imagine replacing the two inductors with a single equivalent inductor $L_{\mathrm{cq}} .$ How is the emf in the series equivalent related to the emfs in the two inductors? What about the currents?]

Key Concepts

Inductance

Inductance is a property of an electrical component that quantifies its ability to store energy in a magnetic field when current flows through it. It plays a central role in inductive circuits and is typically measured in henries (H), reflecting how changing currents induce an electromotive force (emf).

Series Connection of Inductors

When inductors are connected in series, their individual inductances add together to form the equivalent inductance. This is because the same current passes sequentially through each inductor, and the overall voltage drop is the sum of the individual voltage drops across them.

Voltage Summation in Inductive Circuits

In a series configuration, the total induced emf in the equivalent circuit is the sum of the emfs generated by each individual inductor. This is a direct consequence of Faraday’s law of electromagnetic induction, which states that the induced emf in each inductor is related to the rate of change of current flowing through it.

Current Continuity in Series Circuits

In any series circuit, including those with inductors, the same current flows through each component. This principle is essential for analyzing and simplifying the behavior of complex circuits because it ensures that the net effect of multiple inductors can be treated as if they were a single component with an equivalent inductance.

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