Q 12-03-172JEE MainJEE Main 2022 (26 Jul, Shift 1)Medium
Resistances are connected in a meter bridge circuit as shown in the figure. The balancing length $l_1$ is $40\ \text{cm}$. Now an unknown resistance $x$ is connected in series with $P$ and the new balancing length is found to be $80\ \text{cm}$ measured from the same end. Then the value of $x$ will be ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 20
Balance: $\dfrac PQ = \dfrac{40}{60}\Rightarrow Q = \dfrac{4\times60}{40} = 6\ \Omega$.
With $x$ added: $\dfrac{4 + x}{6} = \dfrac{80}{20} = 4\Rightarrow x = 20\ \Omega$.
Solution by Sreeraj P, M.Sc Physics