An electric bulb is rated $220\, V$ and $100\, W$. Power consumed by it when operated on $110\, V$ is ............. $W$.

Heating coils rated at $220\, V$ are available with resistances of $55\,\Omega$,$110\,\Omega$,$220\,\Omega$,and $440\,\Omega$. Which resistance value will produce the maximum power?

Two electric bulbs have resistances in the ratio $1 : 2$. If they are connected in parallel to a constant voltage source,the ratio of power dissipated in them will be:

$A$ wire of resistance $R$ is connected across a cell of emf $\varepsilon$ and internal resistance $r$. The current through the circuit is $I$. In time $t$,the work done by the battery to establish the current $I$ is

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

The resistance of an electrical toaster has a temperature dependence given by $R(T) = R_0[1 + \alpha(T - T_0)]$ in its range of operation. At $T_0 = 300\,K, R = 100\,\Omega$ and at $T = 500\,K, R = 120\,\Omega$. The toaster is connected to a voltage source of $200\,V$ and its temperature is raised at a constant rate from $300\,K$ to $500\,K$ in $30\,s$. The total work done in raising the temperature is: