For the semicircular AC current waveform shown, determine the rms value (A) when the maximum current is a = 2√3/3 A. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

For the semicircular AC current waveform shown, determine the rms value (A) when the maximum current is a = 2√3/3 A. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Use I₍rms₎ = √[(1/T)∫₀ᵀ i²dt]. The drawn waveform has semicircular profile: i²(t) = a²[1 − (t/T₀)²] over its support. Step 2 — Integrate the squared ordinate over one repeat period, using the origin and period from the source plot. Step 3 — Substitute peak a = 2√3/3 A to obtain the printed rms current 1 A. QUALITY FLAG — Period definition is set by the graph, so the waveform graph must remain attached.