The resistor of resistance $R$ is connected to a $25\, V$ supply and the heat produced in it is $25\, J/s$. The value of $R$ is .......... $\Omega$.

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

$A$ bulb has a specification of $1\, kW$ and $250\, V$. The resistance of the bulb 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

$A$ given quantity of water is boiled by an electric heater in $5 \text{ min}$. If the supply voltage of the heater is reduced to half,then the time taken to boil the same quantity of water will be . . . . . . $\text{min}$. (Assume the resistance of the heater remains constant.)

An electric bulb marked as $50 W - 200 V$ is connected across a $100 V$ supply. The present power of the bulb is (in $W$)