What is the approximate percentage value of the ratio of maximum voltage to its rms value in an $LCR$ $AC$ circuit (in $\%$)?

$A$ $110 \, V$ $d.c.$ heater is used on an $a.c.$ source,such that the heat produced is the same as it produces when connected to $110 \, V$ $d.c.$ in the same time intervals. What would be the $r.m.s.$ value of the alternating voltage?

Match the following:
Currents $r.m.s.$ values
$(1) x_0 \sin \omega t$ $(i) x_0$
$(2) x_0 \sin \omega t \cos \omega t$ $(ii) \frac{x_0}{\sqrt{2}}$
$(3) x_0 \sin \omega t + x_0 \cos \omega t$ $(iii) \frac{x_0}{2\sqrt{2}}$

In general,in an alternating current circuit:

An alternating e.m.f. is $e = e_0 \sin \omega t$. In what time will the e.m.f. reach half its maximum value,if $e$ starts from zero? ($T$ = time period)

Find the time required for a $50 \text{ Hz}$ alternating current to reach its $rms$ value from zero. (in $\text{ ms}$)