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:

When a metal conductor connected to the left gap of a meter bridge is heated,the balancing point

The resistance of the meter bridge wire $AB$ in the given figure is $4\,\Omega$. With a cell of emf $\varepsilon_1 = 0.5\,\text{V}$ and rheostat resistance $R_{h1} = 2\,\Omega$,the null point is obtained at point $J$. When the cell is replaced by another one of emf $\varepsilon_2$,the same null point $J$ is found for $R_{h2} = 6\,\Omega$. The emf $\varepsilon_2$ is ................. $\text{V}$.

On interchanging the resistances,the balance point of a meter bridge shifts to the left by $10 \, cm$. The resistance of their series combination is $1 \, k\Omega$. How much was the resistance on the left slot before interchanging the resistances? ................... $\Omega$

When the two known resistances $R$ and $S$ are connected in the left and right gaps of a meter bridge respectively,the null point is found at a distance $l_1$ from the zero end of the meter bridge wire. An unknown resistance $X$ is now connected in parallel with $S$,and the null point is found at a distance $l_2$ from the zero end of the meter bridge wire. The unknown resistance $X$ is:

In the shown arrangement of the meter bridge experiment,if the length $AC$ corresponding to the null deflection of the galvanometer is $x$,what would be its value if the radius of the wire $AB$ is doubled?