In the experimental set up of metre bridge shown in the figure,
In the experimental set up of metre bridge shown in the figure, the null point is obtaine data distance of $40 \mathrm{~cm}$ from A. If a $10 \Omega$ resistor is connected in series with $\mathrm{R}_{1}$, the null point shifts by $10 \mathrm{~cm}$. The resistance that should be connected in parallel with $\left(\mathrm{R}_{1}+10\right) \Omega$ such that the null point shifts back to its initial position is :
Correct Option: , 3
(3) Initially at null deflection $\frac{R_{1}}{R_{2}}=\frac{2}{3}$ ...(1)
Finally at null deflection, when null point is shifted
$\frac{\mathrm{R}_{1}+10}{\mathrm{R}_{2}}=1 \Rightarrow \mathrm{R}_{1}+10=\mathrm{R}_{2} \ldots$
Solving equations (i) and (ii) we get
$\frac{2 R_{2}}{3}+10=R_{2}$
$10=\frac{R_{2}}{3} \Rightarrow R_{2}=30 \Omega$
$\& \mathrm{R}_{1}=20 \Omega$
Now if required resistance is $\mathrm{R}$ then
$\frac{\frac{30 \times R}{30+R}}{30}=\frac{2}{3}$
$R=60 \Omega$