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  4. In the experimental set up of metre bridge shown in the figure, the null point is obtained at a distance of 40 cm from A. If a 10 Ω resistor is connected in series with R1, the null point shifts by 10 cm. The resistance that should be connected in parallel with (R1 + 10)Ω such that the null point shifts back to its initial position is :

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Q. In the experimental set up of metre 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 :Physics Question Image

JEE MainJEE Main 2019Current Electricity

Solution:

$\frac{R_{1}}{R_{2}} = \frac{2}{3} $ ......(i)
$ \frac{R_{1} +10}{R_{2}} = 1 \Rightarrow R_{1} + 10 = R_{2} $ ....(ii)
$ \frac{2R_{2}}{3} + 10 = R_{2} $
$ 10= \frac{R_{3}}{3} \Rightarrow R_{2}= 30 \Omega$
$ \& R_{1} = 20 \Omega $
$ \frac{\frac{30\times R}{30+R}}{30} = \frac{2}{3} $
$ R = 60 \Omega $