For the network shown in Fig, determine the value of $R$ and the current through it, if the current through the branch $AO$ is zero.

 

The potentiometer wire $AB$ shown in Fig. is $40 \mathrm{cm}$ long. Where should the free end of the galvanometer be connected on $AB$ so that the galvanometer may show zero deflection?

The potentiometer wire $AB$ shown in Fig. is $50 \mathrm{cm}$ long. When $AD=30 \mathrm{cm}$, no deflection occurs in the galvanometer. Find $R$.

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.