In the given figure of a meter bridge experiment,the balancing length $AC$ corresponding to null deflection of the galvanometer is $40 \, cm$. What will be the balancing length if the radius of the wire $AB$ is doubled (in $, cm$)?

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? ................... $\Omega$

In order to measure the internal resistance $r_1$ of a cell of emf $E$,a meter bridge of wire resistance $R_0=50 \Omega$,a resistance $R_0/2$,another cell of emf $E/2$ (internal resistance $r$) and a galvanometer $G$ are used in a circuit,as shown in the figure. If the null point is found at $l=72 \text{ cm}$,then the value of $r_1$ is . . . . $\Omega$.

In a meter bridge,the balancing length from the left end is found to be $25 \ cm$. The value of the unknown resistance is (assume,standard resistance of $1 \ \Omega$ is in the right gap). (in $\Omega$)

Two resistances are connected in two gaps of a meter bridge. The balance point is $20 \ cm$ from the zero end. $A$ resistance of $15 \ \Omega$ is connected in series with the smaller of the two. The null point shifts to $40 \ cm$. The value of the smaller resistance in $\Omega$ is

In the meter bridge shown,the length $AB$ for which the deflection in the galvanometer is zero will be ............. $cm$.