Variation of voltage with time is shown in figure.The rms voltage is found to be ,N23V. Find N.

In such cases it is difficult to develop a single equation.Hence, it is usual to consider two equations, one applicable from 0 to 1 ms and another from 1 to 2 ms.For t lying between 0 and 1 ms, V1 = 4. For t lying between 1 and 2 ms, V2 = -4t+4.(a) Vrms=12∫01V12dt+∫12V22dtVrms2=12∫0142dt+∫12(-4t+4)2dt=1216t01+16t3312+|16t|12-32t2212=323Vrms=323=423V. Hence N = 4