In a meter bridge, the wire of length $1\, m$ has a nonuniform cross-section such that, the variation $\frac{{dR}}{{d\ell }}$ of its resistance $R$ with length $\ell $ is $\frac{{dR}}{{d\ell }} \propto \frac{1}{{\sqrt \ell  }}$ 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 $AP$ ? ……………. $m$

Three resistances $P, Q, R$ each of $2 \,\,\Omega$ and an unknown resistance $S$ form the four arms of a Wheatstone bridge circuit. When a resistance of $6 \,\,\Omega$ is connected in parallel to $S$ the bridge gets balanced. What is the value of $S\,?$ …………… $\Omega$

The resistances in $WSB$ circuit shown in the diagram all are different and the current through the galvanometer is zero. If all thermal effects are negligible, the current through the galvanometer will not be zero, when

In Wheatstone's bridge $P = 9\, ohm$, $Q = 11\, ohm$, $R = 4\,ohm$ and $S = 6\,ohm$. How much resistance must be put in parallel to the resistance $S$ to balance the bridge …………… $ohm$

Assertion $(A):$ In a meter bridge experiment, null point for an unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same $p$ as before by decreasing the value of the standard resistance.

Reason $(R):$ Resistance of metal increases with increase in temperature.