If the resistance of the voltmeter is $10000 \,\Omega$ and the resistance of the ammeter is $2 \,\Omega$,find the value of $R$ when the voltmeter reads $12 \,V$ and the ammeter reads $0.1 \,A$.

$A$ $5\ V$ battery with internal resistance $2\,\Omega$ and a $2\,V$ battery with internal resistance $1\,\Omega$ are connected to a $10\,\Omega$ resistor as shown in the figure. Find the current through the $10\,\Omega$ resistor.

The resistance between the terminal points $A$ and $B$ of the given infinitely long circuit will be

The equivalent resistance between points $A$ and $B$ of an infinite network of resistances each of $1\,\Omega$ connected as shown,is

When a resistor of $11 \Omega$ is connected in series with an electric cell,the current flowing in it is $0.5 \ A$. Instead,when a resistor of $5 \Omega$ is connected to the same electric cell in series,the current increases by $0.4 \ A$. The internal resistance of the cell is (in $\Omega$)

In the circuit shown, if the current through the resistor $R$ is $\frac{1}{5} \, A$, the value of $R$ is (in $\Omega$)