$A$ multimeter reads a voltage of a certain $A$.$C$. source as $ 100 \,V $. What is the peak value of voltage of the $A$.$C$. source (in $\,V$)?

An alternating e.m.f. is given by $e = e_0 \sin \omega t$. In what time will the e.m.f. reach half its maximum value, if $e$ starts from zero? (Given: $\sin 30^{\circ} = 0.5$)

What is the $r.m.s.$ value of an alternating current which,when passed through a resistor,produces heat that is thrice the heat produced by a direct current of $2 \ A$ in the same resistor (in $A$)?

The current in a circuit is given by $i = 2\sqrt{t}$. What is the $r.m.s.$ value of the current between $t = 2 \ s$ and $t = 4 \ s$?

The current flowing through an $AC$ circuit is given by $I = 5 \sin(120 \pi t) \text{ A}$. How long will the current take to reach the peak value starting from zero?

An alternating current at any instant is given by $i = [6 + \sqrt{56} \sin (100 \pi t + \frac{\pi}{3})] \ A$. The rms value of the current is . . . . . . . (in $A$)