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An alternating current is given by i(t) = 5 sin(100*pi*t) + 3…
Question
An alternating current is given by i(t) = 5 sin(100*pi*t) + 3 cos(100*pi*t), where i is in amperes and t in seconds. Find the rms value of this current (in amperes).
✓ Verified answer: 4.123106checked by our engine — not a guess
Step-by-step solution
The two terms are sinusoids of the same frequency 90 deg out of phase, so they combine into a single sinusoid of amplitude I0 = sqrt(5^2 + 3^2) = sqrt(34) = 5.83095 A.
The rms value = I0/sqrt(2) = 5.83095/1.41421 = 4.12311 A.
Final answer4.12311
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