For what value of unknown resistance $X$,the potential difference between $B$ and $D$ will be zero in the circuit shown in the figure?

In the Wheatstone's bridge shown,$P = 2\,\Omega$,$Q = 3\,\Omega$,$R = 6\,\Omega$ and $S = 8\,\Omega$. In order to obtain balance,the shunt resistance across '$S$' must be ............. $\Omega$.

In the cube shown,current $i$ enters at $H$ and leaves at $C$. If $i_{AB} = \frac{i}{6}$,$i_{DC} = \frac{2i}{3}$,$i_{HA} = \frac{i}{2}$,$i_{GF} = \frac{i}{6}$,and $i_{HE} = \frac{i}{6}$,choose the branch in which the current is zero.

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 $Omega$)

Three identical batteries each of $emf\ 4\ V$ and negligible internal resistance are connected as shown in the figure. The potential difference between points $A$ and $G$ $(V_A - V_G)$ is ................ $V$.

In the following Wheatstone bridge,$P/Q = R/S$. If key $K$ is closed,then the galvanometer will show deflection: