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