GATE 2024 IN – Question 31
The current drawn is $i(t)=4+30\cos t-20\sin t+15\cos(3t)-10\sin(3t)$ A. Its RMS value is ______ A (one decimal place).
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Show answer and explanation
Correct answer: 27.0 to 30.0
Explanation
Orthogonality of DC, sine, cosine, and distinct harmonics removes all cross terms over a full period.
Therefore $I_{rms}^2=4^2+(30^2+20^2)/2+(15^2+10^2)/2=828.5$. Taking the square root gives **28.8 A**.