Question

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 :

• A. $40\, \Omega$
• B. $60\, \Omega$
• C. $20\, \Omega$
• D. $30\, \Omega$

Answer 1

Answer: (B)

$60\, \Omega$

Answer 2

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