In a meter bridge experiment,$S$ is a standard resistance and $R$ is a resistance wire. It is found that the balancing length is $l = 25 \; cm$. If $R$ is replaced by a wire of half the length and half the diameter of $R$ but of the same material,then the new balancing length $l^{\prime}$ (in $cm$) will be:

In a meter bridge experiment for measuring an unknown resistance '$S$',the null point is obtained at a distance of $30 \ cm$ from the left side,as shown at point $D$. If $R$ is $5.6 \ k\Omega$,then the value of the unknown resistance '$S$' will be $\Omega$.

$(a)$ In a meter bridge,the balance point is found to be at $39.5\; cm$ from the end $A$,when the resistor $Y$ is of $12.5\; \Omega$. Determine the resistance of $X$. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips?
$(b)$ Determine the balance point of the bridge above if $X$ and $Y$ are interchanged.
$(c)$ What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?

In a meter bridge experiment,initially the jockey is at the null point. Now,resistances $R_1$ and $R_2$ are interchanged. The shift in the position of the jockey is ................ $cm$.

Assertion $(A):$ In a meter bridge experiment,the unknown resistance is placed inside an enclosure maintained at a higher temperature. The null point can be obtained at the same position as before by decreasing the value of the standard resistance.
Reason $(R):$ The resistance of a metal increases with an increase in temperature.

$A$ resistance of $20 \Omega$ is connected in the left gap of a metre bridge and an unknown resistance greater than $20 \Omega$ is connected in the right gap. When these resistances are interchanged,the balance point shifts by $20 \text{ cm}$. The unknown resistance is (in $\Omega$)