The magnetic field energy in an inductor changes from maximum to minimum value in 5.0ms when connected to AC source. Find the frequency of the source

To determine the frequency of the AC source connected to the inductor, we need to understand how the magnetic field energy in an inductor behaves when subjected to alternating current. The energy stored in the magnetic field of an inductor varies with time as the current changes direction. In this case, the energy transitions from its maximum to minimum value in a specific time frame, which is 5.0 ms.

Understanding Inductor Behavior in AC Circuits

In an AC circuit, the current through an inductor changes sinusoidally. The magnetic field energy stored in the inductor can be expressed mathematically as:

• Energy (U) = (1/2) * L * I²

Where:

• U is the energy stored in the magnetic field.
• L is the inductance of the inductor.
• I is the current through the inductor.

Energy Variation in AC Circuits

As the current alternates, the energy stored in the inductor reaches its maximum when the current is at its peak and drops to zero when the current is zero. The time taken for the energy to go from maximum to minimum (or zero) corresponds to a quarter of the AC cycle. Therefore, if it takes 5.0 ms to go from maximum to minimum energy, this represents one-fourth of the period (T) of the AC source.

Calculating the Frequency

Since the time taken for the energy to change from maximum to minimum is a quarter of the period, we can express this relationship mathematically:

• T = 4 * (time from max to min) = 4 * 5.0 ms = 20.0 ms

Now, the frequency (f) of the AC source is the reciprocal of the period:

• f = 1 / T

Substituting the period we calculated:

• f = 1 / (20.0 ms) = 1 / (20 x 10^-3 s) = 50 Hz

Final Result

Thus, the frequency of the AC source connected to the inductor is 50 Hz. This means that the current alternates direction 50 times per second, leading to the observed changes in magnetic field energy within the inductor.