$A$ bulb rated at $(100\,W, 200\,V)$ is used on a $100\,V$ line. The current in the bulb is

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P$,$Q$,and $R$ having emfs $E$,$E$,and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

Calculate the voltage across $AB$ terminals in the given circuit.

$A$ resistor is connected to a battery of $12 \text{ V}$ emf and internal resistance $2 \text{ }\Omega$. If the current in the circuit is $0.6 \text{ A}$, the terminal voltage of the battery is: (in $\text{ V}$)

$A$ cell of negligible internal resistance and $e.m.f.$ $2 \ V$ is connected to a series combination of $2 \ \Omega$,$3 \ \Omega$,and $5 \ \Omega$ resistors. The potential difference in volts between the terminals of the $3 \ \Omega$ resistor is:

Water boils in an electric kettle in $15\,\text{min}$ 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 ............. $\text{min}$.