The $Q$ value of a series $L-C-R$ circuit with $L=2 \mathrm{H}$, $C=32 \mu \mathrm{~F}, R=20 \Omega$ is

A resistor of resistance of $100 \Omega$ is connected to an AC source $\varepsilon=10 \sin (250 \pi) t$. The energy dissipated as heat during $t=0$ to $t=1 \mathrm{~ms}$ is approximately.

A $2 \mu \mathrm{~F}$ capacitor is charged to 50 V by a battery. The battery is removed after capacitor if fully charged. At time $t=0$, a 10 mH coil is connected in series with the capacitor. The maximum rate at which the current changes in the circuit is

An AC current is given by the expression, $I(t)=50 \sin (200 \pi t)$ in amperes. The frequency and rms value of the current, respectively are