When the resistance $R$ (indicated in the figure below) is changed from $1 \, k\Omega$ to $10 \, k\Omega$,the current flowing through the resistance $R'$ does not change. What is the value of the resistor $R'$?

In the circuit shown,the current in the $1\,\Omega$ resistor is

Two batteries,one with an $emf$ of $3\,V$ and internal resistance $1\,\Omega$,and the other with an $emf$ of $15\,V$ and internal resistance $2\,\Omega$,are connected in series with a resistance $R$ as shown in the figure. If the potential difference between points $a$ and $b$ is zero,find the resistance $R$ in $\Omega$.

For the circuit shown in the figure,the current through the $6 \Omega$ resistor connected between the junctions $A$ and $B$ is (in $A$)

The readings of ammeters $A_1, A_2$ and $A_3$ will be respectively:

Four resistors $A, B, C$ and $D$ form a Wheatstone bridge. The bridge is balanced when $C = 100 \ \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \ \Omega$. The value of $D$ is: (in $\Omega$)