The four arms of a Wheatstone bridge have resistances as shown in the figure. $A$ galvanometer of $15\, \Omega$ resistance is connected across $BD$. Calculate the current through the galvanometer when a potential difference of $10\, V$ is maintained across $AC$.

The galvanometer has no deflection and the length of wire $AB$ is $350 \, cm$. Then $AC$ equals to ............... $cm$.

If the Wheatstone bridge shown in the figure is balanced,then the values of $R_1$ and $R_2$ are ...... $\Omega$ and ...... $\Omega$ respectively.

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?

In the given circuit,the values of $I_1, I_2, I_3$ are respectively:

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