Heat is produced at a rate given by $H$ in a resistor when it is connected across a supply of voltage $V$. If now the resistance of the resistor is doubled and the supply voltage is made $V / 3$,then the rate of production of heat in the resistor will be

If the current in an electric bulb is changed by $1\%$,then the percentage change in power will be ............. $\%$.

For driving a current of $2\, A$ for $6$ minutes in a circuit, $1000\, J$ of work is to be done. The $e.m.f.$ of the source in the circuit is ................ $V$.

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.

If the resistance of the filament increases with temperature,what will be the power dissipated in a $220\, V- 100\, W$ lamp when connected to a $110\, V$ power supply?

When the power delivered by a $100\,V$ battery is $40\,W$,the equivalent resistance of the circuit is ........... $\Omega$.