The current density in a circular wire is given by $J(r) = (1 \times 10^5 \text{ A/m}^3) r$,where $r$ is the radial distance and the wire's radius is $2 \text{ mm}$. If the potential applied across the wire is $70 \text{ V}$,then the energy consumed by the wire in $1000 \text{ s}$ is:

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.

Which device can convert all electrical energy into heat?

The current flowing through a lamp marked as $50\, W$ and $250\, V$ is ............. $amp$.

In the circuit diagram,the heat produced in resistors $R$,$2R$,and $1.5R$ are in the ratio of:

$A$ resistance $R = 12 \, \Omega$ is connected across a source of $emf$ as shown in the figure. Its $emf$ changes with time as shown in the graph. What is the heat developed in the resistance in the first four seconds (in $, J$)?