In an alternating current (AC) circuit, the relationship between the current and its phasor representation is crucial for understanding the behavior of the system. To illustrate this, consider a current described by a phasor equation. At a specific time of 15 milliseconds, we need to determine the position of the phasor, which begins at 0 degrees.

The angle of the phasor at any time can be calculated using the formula:

θ = ω × t

where θ is the angle in radians, ω is the angular frequency, and t is the time in seconds.

In this case, the angular frequency ω is given as 377 radians per second. To find the angle at 15 milliseconds (or 15 × 10^-3 seconds), we calculate:

θ = 377 × (15 × 10^{-3}) = 5.66 \text{ radians}

To convert this angle from radians to degrees, we use the conversion factor:

Degrees = \frac{θ}{\pi} × 180

Thus, the angle in degrees is:

Degrees = \frac{5.66}{\pi} × 180 \approx 324 \text{ degrees}

With the phasor starting at 0 degrees and rotating counterclockwise, it reaches 324 degrees, which places it in the fourth quadrant of the unit circle. This angle can also be expressed in alternative forms: as 54 degrees from the negative y-axis or as 36 degrees from the positive x-axis. Regardless of the representation, the key takeaway is that the phasor has traveled 324 degrees from its initial position, illustrating the fundamental concept of phasor rotation in AC circuits.