Five equal resistances are connected in a network as shown in the figure. The net resistance between the points $A$ and $B$ 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 circuit given,the correct relation for a balanced Wheatstone bridge is

In the following electrical network, the value of $I$ is (in $\text{ A}$)

Consider the following statements regarding the network shown in the figure.
$(1)$ The equivalent resistance of the network between points $A$ and $B$ is independent of the value of $G$.
$(2)$ The equivalent resistance of the network between points $A$ and $B$ is $\frac{4}{3} R$.
$(3)$ The current through $G$ is zero.
Which of the above statements is/are true?

The figure shows a network of currents. The magnitude of currents is shown in the diagram. The current $i$ will be ................. $A$.