In the circuit shown in the figure,when no current flows through the $5\,\Omega$ resistor,the value of the resistor $X$ will be ........... $\Omega$.

$A$ 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 ............. $\Omega$.

In the given circuit,current $I$ is independent of the resistance $R_6$. Then

See the electrical circuit shown in the adjoining figure. Which of the following equations is a correct equation for it?

The equivalent resistance between $P$ and $Q$ in the given figure is ............... $\Omega$.

The circuit shown is in a steady state. Now,when the switch is closed,the galvanometer shows no deflection. Then the correct relation is: