What is Post Office Box How does it works?

During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at $40.0 \mathrm{cm }$using a standard resistance of $90\mathrm{ }\mathrm{\Omega }$ ,as shown in the figure. The least count of the scale used in the metre bridge is $1\mathrm{mm}$. The unknown resistance is

In a meter bridge, the wire of length $1 m$ has a non-uniform cross-section such that, the variation $\frac{dR}{dl}$ of its resistance $R$ with length $l$ is $\frac{dR}{dl}\propto \frac{1}{\sqrt{l}}.$ Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point $P.$ What is the length $AP?$

In a meter bridge experiment, the null point first found at $40cm$ length of the wire. When a $10\mathrm{\Omega }$ resistor is connected in series in the left gap resistor, the null point shifts by $10cm$ . Now if another resistor $\left(R\right)$ is connected in parallel with the combination $\left(R_1+10\right) \mathrm{\Omega }$ the null point is found at the previous position. Then the resistance $\left(R\right)$ to be connected in parallel is

In a practical Wheatstone's bridge circuit as shown, when one more resistance of $100 \mathrm{\Omega }$ is connected in parallel with an unknown resistance $X$, then ratio $\frac{{\ell }_1}{{\ell }_2}$ become $2$.  ${\ell }_1$ is balance length. $AB$ is a uniform wire. Then, value of $X$ must be

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In a post office box setup find the value of unknown resistance if the graph of galvanometer deflection versus $R$ for the ratio $100:1$ is given as shown