How is the peak current of an alternating current related to its RMS value?

The peak current of an AC is related to its RMS value by a simple mathematical formula.

The RMS value of an AC is the equivalent DC value that produces the same heating effect in a resistor as the AC. It is calculated as the square root of the average of the squares of the instantaneous values of the AC over one cycle. The peak value of an AC is the maximum value of the current over one cycle. The relationship between the peak current and the RMS value is given by the formula I_peak = √2 x I_RMS.

This formula can be derived by considering the power dissipated in a resistor by an AC. The power dissipated is proportional to the square of the current, so the RMS value of the current is used in the calculation. However, the peak value of the current is important for determining the maximum voltage that a circuit can handle, so it is also useful to know.

In practical terms, the RMS value of an AC is the value that is used to rate electrical equipment, such as motors and transformers. The peak value is important for designing circuits and choosing components that can handle the maximum voltage and current that will be present. Understanding the relationship between these values is essential for anyone working with AC circuits.