An inductor is a passive electrical component that stores energy in a magnetic field when electric current flows through it. The fundamental property of an inductor is its inductance, usually denoted by \(L\), which is a measure of its ability to oppose changes in the current flowing through it.

Inductor Voltage Explanation

When the current passing through an inductor changes, a voltage is induced across the inductor. This phenomenon is a direct consequence of Faraday's Law of Induction and Lenz's Law. The magnitude of this induced voltage is directly proportional to the inductance of the inductor and the rate at which the current changes with respect to time.

The voltage induced in an inductor is mathematically represented by the following formula:

\(V_{L} = -L \frac{dI}{dt}\)

Let's break down each term in this formula:

• \(V_{L}\): Represents the voltage induced across the inductor (measured in Volts).
• \(L\): Represents the inductance of the inductor (measured in Henrys, H). This is a constant value for a given inductor.
• \(\frac{dI}{dt}\): Represents the rate of change of current with respect to time (measured in Amperes per second, A/s). This term indicates how quickly the current through the inductor is increasing or decreasing.
• The negative sign in the formula is due to Lenz's Law, which states that the induced voltage will always oppose the change in current that created it. However, when we talk about the "product of" in the options, we are generally referring to the magnitude.

Considering the magnitude of the induced voltage, it is the product of the inductance and the rate of change of current through it.

Evaluating Inductor Options

Let's analyze the given options in the context of the induced voltage:

• Product of its inductance and current through it (\(L \cdot I\)): This product (\(LI\)) represents the magnetic flux linkage through the inductor, not the induced voltage. The energy stored in an inductor is given by \(\frac{1}{2}LI^2\). So, this option is incorrect.
• Ratio of its inductance to current through it (\(L/I\)): This ratio does not represent any standard physical quantity related to the voltage induced in an inductor. So, this option is incorrect.
• Ratio of current through it to its inductance (\(I/L\)): Similar to the previous option, this ratio does not represent the induced voltage. So, this option is incorrect.
• Product of its inductance and rate of change of current through it (\(L \cdot \frac{dI}{dt}\)): This expression directly corresponds to the magnitude of the voltage induced in an inductor, as derived from Faraday's Law of Induction. This aligns perfectly with the fundamental principle of inductors.

Therefore, the voltage induced in an inductor is indeed the product of its inductance and the rate of change of current through it.