# Find the RMS value of the given current waveform.

Find the RMS value of the given current waveform.

### Right Answer is: I = 50/√3 A

#### SOLUTION

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≤ t ≤ T

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

$RMS = \sqrt {\dfrac{1}{T}\mathop \smallint \limits_0^T x{{\left( t \right)}^2}dt}$

$\begin{array}{l} {X_{RMS}} = \sqrt {\dfrac{1}{4}\mathop \smallint \nolimits_0^4 {{(12.5t)}^2}dt} \\ \\ = \sqrt {(\dfrac{{{{12.5}^2}}}{4})\dfrac{{{t^3}}}{3}|_0^4} \\ \\ = \dfrac{{12.5 \times 4}}{{\surd 3}} \end{array}$

I = 50/√3

Thus, RMS current is 50/√3

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