In a meter bridge,the null point is found at a distance of $25\, cm$ from $A$. If now a resistance of $10\,\Omega$ is connected in parallel with $S$,the null point occurs at the midpoint of $AB$. The value of $R$ is ................. $\Omega$. (in $.67$)

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

In a metre-bridge experiment,the balance point is obtained when the gaps are closed by $2 \Omega$ and $3 \Omega$ resistors. $A$ shunt of $x \Omega$ is added in parallel to the $3 \Omega$ resistor to shift the balance point by $22.5 \ cm$. The value of $x$ is: (in $\Omega$)

The resistances in the two arms of a 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,the balancing length from the left end (standard resistance of $1 \, \Omega$ is in the right gap) is found to be $20 \, cm$. The value of the unknown resistance is ............... $\Omega$.

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: