A thin uniform wire $AB$ of length $1 m,$ an unknown resistance $X$ and a resistance of $12\Omega$ are connected by thick conducting strips, as shown in Figure A battery and a galvanometer (with a sliding Jockey connected to it) are also available. Connections are to be made to measure the unknown resistance $X$ using the principle of Wheatstone bridge. Answer the following questions.

After appropriate connection are made, it is found that no deflection takes place in the galvanometer when the sliding jockey touches the wire at a distance of $60 cm$ from $A.$ Obtain the value of the resistance of $X.$

 

The circuit shown in the figure Fig.$5.171$ Is used to measure the value of an unknown resistance $X$ By comparing it with a known resistance $R$ With three different known resistance $R=R_{1,}R=R_2 and R=R_{3.}$ The corresponding null points are obtained at $A,B$ and $C.$ Find which of the above will give the most accurate reading and why ?

Two batteries of different emfs and different internal resistances are connected as shown in Fig.$5.172.$ The voltage across $AB$ in volts is 

In a potentiometer experiment the driver cell has emf $E$ and internal resistance $r.$ The length of the potentiometer wire is $600 cm$ long and its total resistance is $15r.$ What should be the balancing length for a cell of emf $\frac{E}{2}$ and internal resistance $r.$ Also find the current through the galvanometer when the jockey touches at a length of $560 cm$ from the positive end.

Consider a thin square sheet of side $L$ and thickness $t$, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded area in the figure.