The instantaneous current through a resistor is given by i = 6 + 8 sinωt A. Determine the RMS value of the current over one complete cycle.
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Question

The instantaneous current through a resistor is given by i = 6 + 8 sinωt A. Determine the RMS value of the current over one complete cycle.

G1 Physics · Accepted Answer

The current contains a DC component of 6 A and a sinusoidal component of peak value 8 A. Therefore, Iᵣₘₛ² = 6² + (8/√2)² = 36 + 32 = 68. Hence, Iᵣₘₛ = 2√17 A.