A alternating current at any instant is given by $$i = [6 + \sqrt{56}\sin(100\pi t + \pi/3)]\ A$$. The rms value of the current is ______ A.

The current is $$i = 6 + \sqrt{56}\sin(100\pi t + \pi/3)$$

This is a DC component plus an AC component.

DC component: $$I_{DC} = 6$$ A

AC peak value: $$I_0 = \sqrt{56}$$ A

RMS of AC component: $$I_{AC,rms} = \frac{\sqrt{56}}{\sqrt{2}} = \sqrt{28}$$ A

Total RMS: $$I_{rms} = \sqrt{I_{DC}^2 + I_{AC,rms}^2} = \sqrt{36 + 28} = \sqrt{64} = 8$$ A

The answer is 8.