An alternating current is represented by i = 5√2 + 10cos(650πt + π/6) ampere. The RMS value of the current is:
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Question

An alternating current is represented by i = 5√2 + 10cos(650πt + π/6) ampere. The RMS value of the current is:

G1 Physics · Accepted Answer

The current contains a DC component and a sinusoidal AC component: i = I D C I_DC I D ​ C + I₀cos(ωt+φ), with I D C I_DC I D ​ C = 5√2 A, I₀ = 10 A. The mean square value is I r m s 2 I_rms² I r ​ m s 2 = I D C 2 I_DC² I D ​ C 2 + I₀²/2, because the time average of the cross term is zero. Thus, I r m s 2 I_rms² I r ​ m s 2 = (5√2)² + 10²/2 = 50 + 50 = 100. Therefore, I r m s I_rms I r ​ m s = 10 A. Correct option: C.