In a meter bridge experiment,resistances are connected as shown in the figure. The balancing length $l_1$ is $55 \, cm$. Now,an unknown resistance $x$ is connected in series with $P$ and the new balancing length is found to be $75 \, cm$. The value of $x$ is

The resistances in the two gaps of a balanced meter bridge are $X \ \Omega$ and $3X \ \Omega$ respectively. If the resistances are interchanged, the balance point shifts by: (in $\text{ cm}$)

Consider a $72\, cm$ long wire $AB$ as shown in the figure. The galvanometer jockey is placed at $P$ on $AB$ at a distance $x\, cm$ from $A$. The galvanometer shows zero deflection. The value of $x$,to the nearest integer,is ..... $cm$.

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 the experimental setup of a meter bridge shown in the figure,the null point is obtained at a distance of $40\,cm$ from $A$. If a $10\,\Omega$ resistor is connected in series with $R_1$,the null point shifts by $10\,cm$. The resistance that should be connected in parallel with $(R_1 + 10)\,\Omega$ such that the null point shifts back to its initial position is .............. $\Omega$.

In a metre bridge experiment, the balance point is obtained if the gaps are closed by $2 \text{ } \Omega$ and $3 \text{ } \Omega$. $A$ shunt of $X \text{ } \Omega$ is added to $3 \text{ } \Omega$ resistor to shift the balancing point by $22.5 \text{ cm}$. The value of $X$ is