$A$ current of $2\, A$ passing through a conductor produces $80\, J$ of heat in $10$ seconds. The resistance of the conductor is ............ $\Omega$.

The figure shows a thick spherical shell made of a material with electrical conductivity $\sigma$. It has inner and outer radii of $10\ cm$ and $20\ cm$ respectively and is filled with ice inside. Its inner and outer surfaces are kept at different potentials by a battery with internal resistance $r = \frac{2}{\pi}\ \Omega$ and electromotive force $\epsilon = 5\ V$. Find the value of $\sigma$ for which the ice melts at the maximum possible rate,given that $25\%$ of the heat generated by the shell due to Joule heating is used to melt the ice.

An electric heater of resistance $6 \, \Omega$ is run for $10 \, \text{minutes}$ on a $120 \, \text{V}$ line. The energy liberated in this period of time is:

The energy dissipated by a resistor is $10 \, mJ$ in $1 \, s$ when an electric current of $2 \, mA$ flows through it. The resistance is $....... \, \Omega$ (Round off to the Nearest Integer).

$A$ time-varying current $i$ is passed through a resistance $R$ as shown in the figure. The total heat generated in the resistance is

$n$ identical bulbs,each designed to draw a power $P$ from a certain voltage supply,are joined in series across that supply. The total power which they will draw is