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:

The resistances in the two arms of the meter bridge are $5 \,\Omega$ and $R \,\Omega$ respectively. When the resistance $R$ is shunted with an equal resistance,the new balance point is at $1.6\,l_1$. The resistance $R$ is .................. $\Omega$.

In a meter-bridge experiment,a resistance of $18 \Omega$ is connected in the left gap and an unknown resistance $R$ is connected in the right gap. The null point is obtained at $\ell_{1}$ from the left end. If the unknown resistance is replaced by $(\frac{R}{3}) \Omega$,the null point is obtained at $1.5 \ell_{1}$. The unknown resistance $R$ is: (in $Omega$)

In the meter bridge experiment,the length $AB$ of the wire is $1 \ m$. The resistors $X$ and $Y$ have values $5 \ \Omega$ and $2 \ \Omega$ respectively. When a shunt resistance $S$ is connected in parallel to $X$,the balancing point is found to be $0.625 \ m$ from $A$. Then,the resistance of the shunt $S$ is (in $Omega$)

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?

In the circuit shown, a meter bridge is in its balanced state. The meter bridge wire has a resistance of $0.1 \, \Omega/cm$. The value of the unknown resistance $X$ and the current drawn from the battery of negligible internal resistance are: