**Inductor Behavior**

An inductor is a passive electronic component that stores energy in its magnetic field when a current flows through it. It consists of a wire wound into a coil, and the behavior of an inductor is governed by the relationship between the voltage across it and the rate of change of the current flowing through it.

When a sinusoidal voltage is applied to an inductor, the current flowing through it will also be sinusoidal. However, the relationship between the voltage and current in an inductor is not as straightforward as in a resistor or capacitor.

**Inductive Reactance**

The behavior of an inductor is described by its reactance, which is a measure of its opposition to the flow of alternating current. The reactance of an inductor, denoted by XL, depends on the frequency of the applied voltage as well as the inductance of the coil.

The reactance of an inductor can be calculated using the formula:

XL = 2πfL

where XL is the inductive reactance, f is the frequency of the applied voltage, and L is the inductance of the coil.

**Frequency Response**

From the formula for inductive reactance, it can be observed that the reactance is directly proportional to the frequency of the applied voltage. This means that as the frequency increases, the reactance of the inductor also increases.

When a sinusoidal voltage is applied to an inductor with a ferromagnetic core, the inductive reactance will cause the current to lag behind the voltage. This lag is due to the energy stored in the magnetic field of the inductor.

**Answer Explanation**

Based on the above discussion, the current drawn by an inductor with a ferromagnetic core supplied from a sinusoidal voltage source with frequency f will be sinusoidal with the same frequency f. This is because the inductive reactance is directly proportional to the frequency, and as a result, the current will have the same frequency as the applied voltage.

Therefore, option A, which states that the current drawn by the inductor will be sinusoidal with frequency f, is the correct answer.