Effective value of alternating current ?

The effective value of an alternating current (AC) is the equivalent value of the current that would produce the same amount of power dissipation in a resistive load as a direct current (DC) of the same value. It is also known as the root mean square (RMS) value of the AC current. The effective value of an AC current is calculated using the formula:

Effective value = Peak value / √2

Where the peak value is the maximum value of the AC current waveform. The effective value is important for determining the power dissipation and heating effects of an AC current in a circuit.

The effective value of an alternating current (AC) is the value of a direct current (DC) that would produce the same amount of heating in a resistor over a given period of time. It is also known as the root mean square (rms) value.

The effective value of an alternating current is given by the following equation:


$$ I_{eff} = \sqrt{\frac{1}{T} \int_0^T i^2(t) dt }$$


where:

- $$I_{eff}$$ is the effective value of the current
- $$i(t)$$ is the instantaneous value of the current
- $$T$$ is the period of the current

The effective value of an alternating current is always less than the peak value of the current. For a sinusoidal alternating current, the effective value is equal to the peak value divided by the square root of 2:


$$ I_{eff} = \frac{I_{peak}}{\sqrt{2}} $$


The effective value of an alternating current is important because it is the value that is used to calculate the power dissipated in a resistor. The power dissipated in a resistor is given by the following equation:


$$ P = I^2R $$


where:

- $$P$$ is the power dissipated
- $$I$$ is the current
- $$R$$ is the resistance

If the current is an alternating current, then the effective value must be used in the above equation.