$A$ 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

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?

$A$ $100\, W$ bulb working on $200\, V$ and a $200\, W$ bulb working on $100\, V$ have:

An incandescent bulb has a thin filament of tungsten that is heated to high temperature by passing an electric current. The hot filament emits black-body radiation. The filament is observed to break up at random locations after a sufficiently long time of operation due to non-uniform evaporation of tungsten from the filament. If the bulb is powered at constant voltage, which of the following statement(s) is(are) true?
$(A)$ The temperature distribution over the filament is uniform
$(B)$ The resistance over small sections of the filament decreases with time
$(C)$ The filament emits more light at higher band of frequencies before it breaks up
$(D)$ The filament consumes less electrical power towards the end of the life of the bulb

$A\, 5\, ^oC$ rise in the temperature is observed in a conductor by passing some current. When the current is doubled,then the rise in temperature will be equal to ............. $^oC$.

What is the maximum voltage that can be safely applied across a resistor of $196 \,\Omega - 1 \,W$ rating? .......... $volt$