SSE JE Electrical Engineering 24 March 2021 Shift 1 Paper

For a periodic waveform given by x(t) with the fundamental period as ‘T,’ the RMS value is defined as: $\mathrm{RMS}=\sqrt{\frac{1}{\mathrm{T}}\underset{0}{\overset{\mathrm{T}}{\int }}\mathit{x}{\left(\mathrm{t}\right)}^2\mathrm{dt}}$
Sequence is repeating at time period of T = 4 sec.
$\therefore \mathit{x}\left(\mathit{t}\right)=\left(\frac{50}{4}\right)\mathit{t}=12.5\mathit{t}$
Where x(t) is the function of the curve between $0\le \mathit{t}\le \mathrm{T}$ $\mathrm{RMS}=\sqrt{\frac{1}{\mathrm{4}}\underset{0}{\overset{4}{\int }}{\left(12.5\mathit{t}\right)}^2\mathrm{dt}}$   $\sqrt{{\left[{\left(\frac{12.5}{4}\right)}^2\frac{{\mathit{t}}^3}{3}\right]}_0^4}$ $=\frac{12.5\times 4}{\sqrt{3}}$ $=\frac{50}{\sqrt{3}}$
Thus, rms current $\mathrm{I}=\frac{50}{\sqrt{3}}\mathrm{A}$