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 ................. $\text{V}$.

In the meter bridge shown,the resistance $X$ has a negative temperature coefficient of resistance. Neglecting the variation in other resistors,when current is passed for some time in the circuit,the balance point should shift towards:

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

When two resistances $R_1$ and $R_2$ are connected in series and introduced into the left gap of a meter bridge and a resistance of $10 \ \Omega$ is introduced into the right gap,a null point is found at $60 \ cm$ from the left side. When $R_1$ and $R_2$ are connected in parallel and introduced into the left gap,a resistance of $3 \ \Omega$ is introduced into the right gap to get a null point at $40 \ cm$ from the left end. The product $R_1 R_2$ is $............. \ \Omega$.

In a meter bridge experiment,when resistance $X$ is in the left gap and $Y$ is in the right gap,the null point is found at $20 \ cm$ from the left end. If $X < Y$,what will be the new position of the null point from the same end if a resistance of $4X$ is placed in the left gap instead of $X$?

In a meter bridge experiment,a null point is obtained at $40 \ cm$ from one end of the wire when resistance $X$ is balanced against another resistance $Y$. If $X < Y$,then the new position of the null point from the same end,if one decides to balance a resistance of $3X$ against $Y$,will be close to .............. $cm$.