A current rises steadily from $0$ to $I_0$ during each period and then drops back to zero at once, again and again, as shown in the graph (a sawtooth wave). Its average value and its root-mean-square (rms) value over a period are

Fig. 1: A sawtooth current: it rises steadily from 0 to I0 during each period T and then drops back to zero at once.