In a Wheatstone bridge,three resistances $P, Q$ and $R$ are connected in the three arms and the fourth arm is formed by two resistances $S_1$ and $S_2$ connected in parallel. The condition for the bridge to be balanced is

The value of current $I$ in the electrical circuit as given below,when potential at $A$ is equal to the potential at $B$,will be . . . . . . $A$.

In the Wheatstone's bridge (shown in figure) $X = Y$ and $A > B$. The direction of the current between $a$ and $b$ will be

As shown in the figure,a $5\,V$ battery with $2\,\Omega$ internal resistance and a $2\,V$ battery with $1\,\Omega$ internal resistance are connected to a $10\,\Omega$ resistor. The current flowing through the $10\,\Omega$ resistor is:

Two resistances $R_1 = X \Omega$ and $R_2 = 1 \Omega$ are connected to a wire $AB$ of uniform resistivity,as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \text{ mm}$ at $A$ to $1 \text{ mm}$ at $B$. $A$ galvanometer $(G)$ connected to the center of the wire,$50 \text{ cm}$ from each end along its axis,shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is:

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.