Calculate the value of unknown resistance $X$ and the current drawn by the circuit, assuming that no current flows through the galvanometer. Assume the resistance per unit length of the wire $AB$ to be $0.01 \mathrm{\Omega }/\mathrm{cm}$. Fig.

 

In fig, $P=3 \mathrm{\Omega }$, $Q=2 \mathrm{\Omega }$, $R=6 \mathrm{\Omega }$, $S=4 \mathrm{\Omega }$ and $X=5 \mathrm{\Omega }$. Calculate the current $I$.

Each resistor $r$ shown in Fig. has a resistance of $10 \mathrm{\Omega }$ and the battery has an emf of $6 \mathrm{V}$. Find the current supplied by battery.

Find the equivalent resistance between the points $X$ and $Y$ of the network shown in Fig.

Fig. shows experimental setup of a metre bridge. When the two unknown resistances $X$ and $Y$ are inserted, the null point $D$ is obtained $40 \mathrm{cm}$ from the end $A$. When a resistance of $10 \mathrm{\Omega }$ is connected in series with $X$, the null point shifts by $10 \mathrm{cm}$. Find the position of the null point when the $10 \mathrm{\Omega }$ resistance is instead connected in series with resistance '$Y$'. Determine the values of the resistances $X$ and $Y$.