What is the potential difference across a 10 mH inductor if the current through the inductor drops from 150 mA to 50 mA in 10 μs? What is the direction of this potential difference? That is, does the potential increase or decrease along the direction of the current?

Verified step by step guidance

1. Start by recalling the formula for the potential difference (voltage) across an inductor: $V=L\frac{\mathrm{dI}}{\mathrm{dt}}$, where $L$ is the inductance, $\mathrm{dI}$ is the change in current, and $\mathrm{dt}$ is the time interval over which the current changes.
2. Determine the change in current, $\mathrm{dI}$, by subtracting the final current from the initial current: $\mathrm{dI}=I{\mathrm{initial}}_{}-I{\mathrm{final}}_{}$. Substitute the given values: $I{\mathrm{initial}}_{}=150 \mathrm{mA}$ and $I{\mathrm{final}}_{}=50 \mathrm{mA}$. Convert these values to amperes before calculating.
3. Substitute the inductance, $L$, and the time interval, $\mathrm{dt}$, into the formula. The inductance is given as $L=10 \mathrm{mH}$, which should be converted to henries, and the time interval is $\mathrm{dt}=10 \mathrm{\mu s}$, which should be converted to seconds.
4. Calculate the potential difference using the formula: $V=L\frac{\mathrm{dI}}{\mathrm{dt}}$. Ensure all units are consistent (henries for inductance, amperes for current, and seconds for time).
5. To determine the direction of the potential difference, recall Lenz's Law: the induced voltage in an inductor opposes the change in current. Since the current is decreasing, the potential difference will increase along the direction of the current to oppose the drop in current.

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. The unit of inductance is the henry (H), and in this case, the inductor has a value of 10 mH (millihenries). Inductance is crucial for understanding how inductors respond to changes in current.

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. For inductors, this means that when the current through the inductor changes, it generates a voltage (potential difference) across its terminals. The induced voltage is proportional to the rate of change of current, which is essential for calculating the potential difference in this scenario.

Lenz's Law

Lenz's Law states that the direction of the induced current (and thus the potential difference) in an inductor will oppose the change in current that created it. This means that if the current through the inductor decreases, the induced potential difference will act in a direction that tries to maintain the current flow. Understanding Lenz's Law helps determine whether the potential difference increases or decreases along the direction of the current.