Consider the circuit shown in the figure.

In the given circuit,for maximum power to be transferred from a battery with an internal resistance of $4\, \Omega$,what should be the value of $R$ in $\Omega$?

$A$ $100 \ V$ voltmeter having a resistance of $20 \ k\Omega$ is connected in series with a very high resistance $R$. When it is connected to a $110 \ V$ line,it reads $5 \ V$. What is the value of $R$?

In the circuit shown,the resistance $r$ is a variable resistance. If for $r = fR$,the heat generation in $r$ is maximum,then the value of $f$ is:

An electrical circuit consists of ten $100 \,\Omega$ resistors. Out of these $10$ resistors,a group of $n_1$ resistors are connected in parallel and another group of $n_2$ resistors are separately connected in parallel. These two groups are then connected in series and this combination is connected to a voltage source of $100 \,V$. If the net current through the circuit is $2.5 \,A$,the values of $n_1$ and $n_2$ are:

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