An electric fan and a heater are marked as $100 \ W, 220 \ V$ and $1000 \ W, 220 \ V$ respectively. The resistance of the heater is

$A$ steady current $I$ flows through a wire of radius $r$,length $L$ and resistivity $\rho$. The current produces heat in the wire. The rate of heat loss in a wire is proportional to its surface area. The steady temperature of the wire is independent of

What is the value of $1 \, kWh$ in Joules?

How many calories of heat will be produced approximately in a $210\, W$ electric bulb in $5$ minutes?

The material of a fuse wire should have:

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.