In the circuit,$E_1 = E_2 = E_3 = 2 \text{ V}$ and $R_1 = R_2 = 4 \text{ } \Omega$. Then the current flowing through $E_2$ is

The current between $B$ and $D$ in the given figure is .............. $A$.

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:

The current $i$ in the circuit given below is

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 $R$.

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