How can instantaneous current at any given degree in an AC cycle be represented?

The representation of instantaneous current in an alternating current (AC) cycle is effectively modeled by utilizing the sine function. In an AC system, the current varies sinusoidally over time, which can be expressed as a function of the phase angle (θ).

The formula relating instantaneous current (Ii) to the peak current (Ipk) and the angle (θ) is formulated as Ii = Ipk * sin(θ). This indicates that at any given degree within the AC cycle, the instantaneous current can be derived by multiplying the peak current by the sine of the angle. The sine function is fundamental in defining how the current fluctuates throughout the cycle, corresponding to the cyclical nature of AC signals.

In contrast, the other formulas are not representative of the correct relationship for instantaneous current in the context of AC. For example, the use of cosine would imply a phase shift, which pertains to the voltage in an AC circuit but does not accurately define the instantaneous current as a function of time reflecting the sine wave's shape. The tangent function does not capture the cyclic behavior of AC currents either, and dividing by the angle does not yield a real physical quantity representative of current.