The root mean square value of the alternating current is equal to

For the $RC$ circuit shown, the resistance is $R = 10.0\ W$, the capacitance is $C = 5.0\ F$ and the battery has voltage $\xi= 12$ volts . The capacitor is initially uncharged when the switch $S$ is closed at time $t = 0$. At some time later, the current in the circuit is $0.50\ A$. What is the magnitude of the charge across the capacitor at that moment?.......$µC$

An alternating voltage $V = 300\sqrt 2 sin(100t)$ is connected to a $1\ \mu F$ capacitor through an $AC$ ammeter. The reading of the ammeter will be.....$mA$

A resistance of $20$ ohms is connected to a source of an alternating potential $V = 220\,sin\,(100\,\pi t)$. The time taken by the current to change from its peak value to r.m.s value is

The alternating current is given by

${i}=\left\{\sqrt{42} \sin \left(\frac{2 \pi}{{T}} {t}\right)+10\right\} {A}$

The $r.m.s.$ value of this current is ${A}$

Two cables of copper are of equal lengths. One of them has a single wire of area of cross-section $A$, while other has $10$ wires of cross-sectional area $A / 10$ each. Give their suitability for transporting $A.C.$ and $D.C.$