The figure shows currents in a part of an electric circuit. Then the current $I$ is: (in $A$)

In the circuit shown in the figure,all the resistances are identical and each has the value $r \ \Omega$. The equivalent resistance of the combination between the points $A$ and $B$ will remain unchanged even when the following pairs of points marked in the figure are connected through a resistance $R$.

If the potential difference between $B$ and $D$ is zero,the value of $x$ is $\frac{1}{n} \Omega$. The value of $n$ is .......

The Wheatstone bridge shown in the diagram is balanced. If $P_3$ is the power dissipated by $R_3$ and $P_1$ is the power dissipated by $R_1$,then the ratio $\frac{P_3}{P_1}$ is

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 in the figure,if no current flows through the galvanometer when the key $K$ is closed,the bridge is balanced. The balancing condition for the bridge is