root mean square current is defined as the value of
What is the root mean square current defined as?
Answer:
Root mean square (RMS) current is defined as the value of the current which, when passed through a resistor for a given time, produces the same heating effect as an equivalent direct current. It is the effective current in an AC circuit that produces the same heating effect as a DC circuit. In other words, the RMS value of an AC current is the DC current that would dissipate the same amount of power in a resistive load as the AC current does.
For a sinusoidal voltage or current, the RMS value can be calculated by taking the square root of the mean of the square of the values of the waveform over one cycle. The formula to calculate the RMS value for a function f(t) over one period T is given by:
I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} [f(t)]^2 dt}
RMS values are particularly useful for comparing AC and DC quantities or for calculating power in AC circuits. In summary, RMS current provides a consistent measure of the effective heating power in a circuit with an alternating current.