The average value of an oscillating electric current over one period may be zero. For example, 2nt suppose that the current is described by a simple sinusoid: i(t) = sin 2πt/T where T is the period.
The average value of this function can be determined by the following equation:
i=∫ν0^T(2πt/T)dt/T-0 = -cos(2π) + cos0/T=0
Despite the fact that the net result is zero, such current is capable of performing work and generating heat . Therefore, electrical engineers often characterize such current by
I RMS = √1\T∫ν0^Ti^2(t)dt
where i(t) = the instantaneous current. Calculate the RMS or root-mean-square current of the waveform shown in following figure using the trapezoidal rule, Simpson's 1/3 rule, Simpson's 3/8 rule for T =1 s taking n = 6.
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