An electric bulb is designed to draw power $P_0$ at voltage $V_0$. If the voltage is $V$,it draws a power $P$. Then:

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 ................ $V$.

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

Two electric bulbs whose resistances are in the ratio of $1:2$ are connected in series. The powers dissipated in them have the ratio:

The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is:

In the figure shown,the power generated in $y$ is maximum when $y = 5\,\Omega$. Then $R$ is