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

During an experiment with a meter bridge,the galvanometer shows a null point when the jockey is pressed at $40.0 \ cm$ using a standard resistance of $90 \ \Omega$,as shown in the figure. The least count of the scale used in the meter bridge is $1 \ mm$. The unknown resistance is:

In a meter bridge (Figure), the null point is found at a distance of $33.7 \; cm$ from $A$. If now a resistance of $12 \; \Omega$ is connected in parallel with $S$, the null point occurs at $51.9 \; cm$. Determine the values of $R$ and $S$.

If the balance point is obtained at the $35^{th} cm$ in a meter bridge,the resistances in the left and right gaps are in the ratio of:

In a meter bridge,a $30 \Omega$ resistance is connected in the left gap and a pair of resistances $P$ and $Q$ in the right gap. Measured from the left,the balance point is $37.5 \text{ cm}$ when $P$ and $Q$ are in series,and $71.4 \text{ cm}$ when they are in parallel. The values of $P$ and $Q$ (in $\Omega$) are:

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 $\Omega$)