Two bulbs of equal wattage, one having carbon filament and the other having a tungsten filament are connected in series to the mains, then

From where electrical power derive ? Explain it.

The charge flowing through a resistance $R$ varies with time as $Q = 2t - 8t^2$. The total heat produced in the resistance is (for $0 \leq t \leq \frac{1}{8}$)

Two bulbs are in parallel and they together consume $48\, W$ from a battery of $6\, V$. The resistance of each bulb is ............ $\Omega$

An electric bulb rated for $500\, watts$ at $100\, volts$ is used in a circuit having a $200-volt$ supply. The resistance $R$ that must be put in series with the bulb, so that the bulb draws $500\, W$ is .................. $\Omega$

Water boils in an electric kettle in $15\,\min$ after switching on. If the length of the heating wire is decreased to $2/3$ of its initial value, then the same amount of water will boil with the same supply voltage in ............. $min$