Two wires '$A$' and '$B$' of the same material have lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. If the two wires are connected in parallel to a battery,the ratio of heat produced in wire '$A$' to that in wire '$B$' will be:

On giving $220\,V$ to a resistor,the power dissipated is $40\,W$. The value of the resistance is ............... $\Omega$.

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

An electric lamp is marked $60\, W$, $230\, V$. The cost of $1\, kWh$ of energy is Rs. $1.25$. The cost of using this lamp for $8$ hours a day for $30$ days is Rs. ...............

Which of the following curves represents the relationship between the heat produced in a resistor and the current flowing through it?

The number of electrons moving per second through the filament of a lamp of $60 \text{ W}$ operating at $120 \text{ V}$ is nearly $(e = 1.6 \times 10^{-19} \text{ C})$