$A$ Wheatstone bridge is used to determine the value of an unknown resistance $X$ by adjusting the variable resistance $Y$ as shown in the figure. For the most precise measurement of $X$,the resistances $P$ and $Q$:

In the given circuit,the galvanometer shows zero deflection. What is the value of $R$ in $\Omega$?

Calculate the current in wire $BD$ in the given circuit. (in $, A$)

Seven resistances are connected as shown in the figure. The equivalent resistance between $A$ and $B$ is ............... $\Omega$.

The four arms of a Wheatstone bridge (Figure) have the following resistances: $AB = 100 \; \Omega$,$BC = 10 \; \Omega$,$CD = 5 \; \Omega$,and $DA = 60 \; \Omega$. $A$ 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 $AC$.

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor,an electrical arrangement shown in the figure is prepared. The arm $BC$ is made up of the semiconductor. The experiment is being conducted at $25^{\circ} C$ and the resistance of the semiconductor arm $BC$ is $3 \ m\Omega$. Arm $BC$ is cooled at a constant rate of $2^{\circ} C / s$. If the galvanometer $G$ shows no deflection after $10 \ s$,then $\alpha$ is: