The value of current in the $6 \,\Omega$ resistance is $....\,A$

In the adjoining circuit,the battery $E_1$ has an $e.m.f.$ of $12 \, V$ and zero internal resistance,while the battery $E$ has an $e.m.f.$ of $2 \, V$. If the galvanometer $G$ reads zero,then the value of the resistance $X$ in $\Omega$ is

The current through the wire $XY$ of the circuit shown is ................ $A$.

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 $R$.

$A$ uniform wire of length $200 \, cm$ is connected to a battery, two resistors and a galvanometer as shown in the figure. The galvanometer shows null deflection when the jockey $J$ is at $80 \, cm$ from point $A$. If the resistor $R_2$ is shunted with $30 \, \Omega$ resistance, the galvanometer shows null deflection when the jockey $J$ is at $100 \, cm$ from point $B$. Then the values of $R_1$ and $R_2$ respectively are

Kirchhoff's second law is based on the law of conservation of: