Find the RMS value of the given current waveform.

Concept:

For a periodic waveform given by x(t) with the fundamental period as ‘T,’ the RMS value is defined as:

$RMS=\sqrt{\frac{1}{T}\underset{0}{\overset{T}{\int }}x{\left(t\right)}^{2}dt}$

Calculation:

Sequence is repeating at time period of T = 4 sec.

∴ x(t) = ( 50 / 4) t = 12.5 t

Where x(t) is the function of the curve between $0\le t\le T$

RMS value of waveform, 

 $X_{RMS}=\sqrt{\frac{1}{4}{\int }_0^4(12.5t{)}^{2}dt}$

$=\sqrt{(\frac{{12.5}^2}{4})\frac{t^3}{3}{|}_0^4}$

$=\frac{12.5\times 4}{\surd 3}$

$=\frac{50}{\surd 3}$

Thus, rms current $I=\frac{50}{\sqrt{3}}$A

Additional Information

The term RMS ONLY refers to time-varying sinusoidal voltages, currents, or complex waveforms where the magnitude of the waveform changes over time.

RMS value is defined as the “amount of AC power that produces the same heating effect as an equivalent DC power".