Which formula relates inductance to the induced emf and the rate of change of current?

The formula that relates inductance to the induced electromotive force (emf) and the rate of change of current is expressed as L = V/(di/dt). In this context, inductance (L) is defined as the proportionality constant that describes how much emf is induced in a circuit when there is a change in current over time.

When current through an inductor changes, an emf is induced in the opposite direction to the change. This phenomenon, which is a result of Faraday's Law of Electromagnetic Induction, can be quantified by dividing the induced emf (V) by the rate at which the current is changing (di/dt). As such, inductance measures the efficiency and effectiveness of an inductor to store energy in the magnetic field generated by the flow of electric current.

In practice, this means that a larger value of inductance corresponds to a greater emf generated for a given rate of change in current. Thus, the formula effectively captures the relationship between these fundamental properties of inductors in electrical circuits, emphasizing the role of inductance in their operation and behavior.