The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate.
(a) The potential between points a and b is Vab = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?

Verified step by step guidance

1. Identify the given values: inductance L = 0.260 H and potential difference V_{ab} = 1.04 V with point a at higher potential.
2. Recall the formula for the potential difference across an inductor: V = L \frac{dI}{dt}, where \frac{dI}{dt} is the rate of change of current.
3. Since V_{ab} is positive and point a is at a higher potential, the induced emf opposes the increase in current according to Lenz's Law.
4. Determine the direction of the induced emf: if the current were increasing, the induced emf would oppose this increase, making point a higher in potential.
5. Conclude that since point a is at a higher potential, the current must be increasing.

Key Concepts

Inductance

Inductance is a property of an electrical component, typically a coil or inductor, that quantifies its ability to store energy in a magnetic field when an electric current flows through it. It is measured in henries (H) and is defined as the ratio of the induced electromotive force (emf) to the rate of change of current. In this case, the inductor has an inductance of 0.260 H, which influences how the current changes over time.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in that circuit. This principle is crucial for understanding inductors, as the changing current in the inductor creates a changing magnetic field, which in turn induces a voltage across the inductor. The direction of the induced emf opposes the change in current, as described by Lenz's Law.

Voltage and Current Relationship in Inductors

In an inductor, the voltage across the inductor (V) is related to the rate of change of current (di/dt) through the equation V = L(di/dt), where L is the inductance. If the voltage is positive and the current is increasing, the induced emf opposes the increase, suggesting that the current is decreasing. Conversely, if the current is decreasing, the induced emf acts to maintain the current, indicating that the current is indeed decreasing in this scenario.