Question

Find the average and rms values of the saw-tooth wave form as shown in figure.


and report the nearest integer of the sum of two.

Answer 1

Since voltage increases linearly, so
$V_{av}=\frac{0+50}{2}=25V$
Let V be the instantaneous value of voltage between 0 to 2 s, then $V=\frac{50}{2}t=25t$
The rms or effective value of the voltage is
$V_{rms}^2=\frac{1}{T}{\int }_0^T{V}^{2}dt=\frac{1}{2}{\int }_0^2(25t{)}^{2}dt=\frac{625}{2}{\int }_0^2{t}^{2}dt=\frac{625}{2}{\left|\frac{t^3}{3}\right|}_0^2=833.3V$
$\therefore V_{rms}=28.9V$.

Why this question? Caution: r.m.s. is not the underroot of square of average, but underroot of average of squares of all values!