In the given electrical network, the value of resistance ' $R$ ' when the current in the galvanometer will be zero, is

In the circuit shown in the figure, $P \neq R$. The reading of the galvanometer remains the same with switch ' $S$ ' open or closed. Then

If an ammeter is to be used in place of a galvanometer then we must connect

The length of a potentiometer wire is ' $L$ ' . A cell of e.m.f. $E$ is balanced at a length $\frac{L}{5}$ from the positive end of the wire. If the length of the wire is increased by $\frac{L}{2}$, the same cell will give balance point at distance ' $x$ '. The value of ' $x$ ' is