If $I_1, I_2, I_3$ and $I_4$ are the respective $r.m.s$. values of the time varying currents as shown in the four cases $I, II, III$ and $IV$. Then identify the correct relations.

An $AC$ current is given by $I = I _{1} \sin \omega t + I _{2} \cos \omega t$. A hot wire ammeter will give a reading

The effective value of current $i = 2\, sin\, 100\, \pi\, t + 2 \,sin(100\, \pi \,t + 30^o)$ is :

An alternating voltage $\mathrm{V}(\mathrm{t})=220 \sin 100 \ \pi \mathrm{t}$ volt is applied to a purely resistive load of $50\ \Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

An alternating voltage $E = 200\sqrt 2\, \sin\, (100\,t)$ is connected to a $1$ microfarad capacitor through an ac ammeter. The reading of the ammeter shall be......$mA$

The voltage of an $ac$ supply varies with time $(t)$  as $V = 120\sin 100\,\pi \,t\cos 100\pi \,t.$ The maximum voltage and frequency respectively are