The resistance of a hot tungsten filament is about $10$ times its cold resistance. What will be the resistance of a $100\, W$ and $200\, V$ lamp when not in use? (in $\Omega$)

$A$ cell has an emf of $2 \, V$ and an internal resistance of $0.1 \, \Omega$. It is connected to an external resistance of $3.9 \, \Omega$. The terminal voltage across the cell will be: (in $V$)

An infinite ladder network of resistors is shown in the figure. If $R_1 = 1 \, \Omega$ and $R_2 = 2 \, \Omega$,then the equivalent resistance between $A$ and $B$ is ................ $\Omega$.

$A$ voltmeter of resistance $998\ \Omega$ is connected to a cell of $emf$ $2\ V$ and internal resistance $2\ \Omega$. The error in the measurement of $emf$ will be:

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 ............. $\text{min}$.

Two batteries of e.m.f $4 \text{ V}$ and $8 \text{ V}$ with internal resistance $1 \Omega$ and $2 \Omega$ respectively are connected in a circuit with a resistance of $9 \Omega$ as shown in the figure. The current and potential difference between the points $P$ and $Q$ is