- 2071 Chaitra · 6 marks
RMS of triangular current waveform
Short answer
For a triangular wave of peak Im, rms value = Im/√3. With Im=18A, Irms = 18/1.732 = 10.39 A.
Calculate the rms value of current of the following triangular waveform. [Figure: train of triangular pulses of peak 18 A; first triangle from 0 to 2π peaking at π; second from 2π to 4π peaking at 3π.]
From the figure: triangles of peak 18 A. The first rises from 0 at θ = 0 to 18 A at π and falls to 0 at 2π; the second repeats from 2π to 4π. So the period is 2π.
Rising portion: i = Im θ/π, with Im = 18 A. The falling portion is its mirror image, so the mean square over 0 to π equals that over the whole cycle.
I_rms² = (1/π) ∫₀^π (Im θ/π)² dθ = (Im²/π³) × (π³/3) = Im²/3
I_rms = Im/√3 = 18 / 1.732
I_rms = 10.39 A
(Average value = Im/2 = 9 A, so the form factor is 10.39/9 = 1.155.)
✓ Answer checked by Claude Opus 5.5 (high effort)
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