What is the formula of current in AC?

Alternating Current Formula: Understanding the Sinusoidal Flow

Alternating current (AC) is a type of electrical current that changes direction periodically, unlike direct current (DC), which flows in only one direction. This oscillation in AC is represented by a sinusoidal waveform, which can be described mathematically by the following formula:

I = I<sub>m</sub> sin(2πft)

where:

• I is the instantaneous current value
• I_m is the peak current (maximum value)
• f is the frequency (number of oscillations per second)
• t is the time

This equation indicates that the current in an AC circuit fluctuates from zero to its peak value and then back to zero, following a sinusoidal pattern. The frequency determines the rate of oscillation, with a higher frequency resulting in a faster oscillation.

Root-Mean-Square (RMS) Current

In practical applications, it is often more useful to deal with the average value of the alternating current, known as the effective current or root-mean-square (RMS) current. RMS current represents the heating effect of the AC current and is calculated as follows:

I<sub>rms</sub> = I<sub>m</sub>/√2

RMS current is typically used for calculations involving AC power and voltage, as it is proportional to the average power dissipated in a circuit.

Comparison with Direct Current

In contrast to AC, direct current flows in a constant direction, meaning its instantaneous value remains the same over time. As a result, the peak current, frequency, and RMS current are all equal for DC, and the sinusoidal formula does not apply.

Conclusion

The formula for alternating current, I = I_m sin(2πft), along with the concept of RMS current, provides a comprehensive understanding of the sinusoidal nature of AC. This knowledge is essential for analyzing and designing AC circuits and systems, where the oscillatory flow of current plays a crucial role in various electrical applications.