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.

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 ................ $V$.

$A$ Wheatstone's bridge is balanced with a resistance of $625\, \Omega$ in the third arm,where $P, Q$ and $S$ are in the $1^{st}, 2^{nd}$ and $4^{th}$ arm respectively. If $P$ and $Q$ are interchanged,the resistance in the third arm has to be increased by $51\,\Omega$ to secure balance. The unknown resistance in the fourth arm is ............. $\Omega$.

Find the potential difference $(V_A - V_B)$ for the given circuit.

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 $\Omega$)

In the given circuit,if the voltage between points $B$ and $D$ is zero,then what is the value of resistance $x$ in $\Omega$?