A coil of self inductance $L=1 \mathrm{H}$ & resistance $r=4 \mathrm{\Omega }$ is connected in series with a variable resistance $R$ and an a.c. source with $\omega =3 \mathrm{rad} {\mathrm{s}}^{-1}$ as shown in the figure. What should be the value of $R$ (in $\mathrm{\Omega }$) so that the rate of heat loss through $R$ is maximum?

The velocity of an electron at point $A$ is $V_0$, where the cross-sectional area is$a$. The velocity of the electron at the end of contraction at point $B$, where the cross-sectional area is $2a$, is $V_1$. Find the correct option.

A battery of $10 \mathrm{V}$ and negligible internal resistance is connected across the diagonally opposite corner of a cubical network consisting of $12$ resistors each of resistance $1 \mathrm{\Omega }$. The total current $I$ in the circuit external to the network is: