Q 12-03-253JEE MainJEE Main 2019 (10 Apr, Shift 1)Medium
In a meter bridge experiment, a resistance box $R$ is in the left gap and an unknown resistance $X$ in the right gap; the balance length $l$ is measured from the left end of the wire. The observations are:
$$\begin{array}{ccc} \text{S. No.} & R\,(\Omega) & l\,(\text{cm}) \\ \hline 1 & 1000 & 60 \\ 2 & 100 & 13 \\ 3 & 10 & 1.5 \\ 4 & 1 & 1.0 \end{array}$$
Which of the readings is inconsistent?
Answer: (D) 4
At balance $\dfrac RX = \dfrac{l}{100-l}$, so $X = R\,\dfrac{100-l}{l}$:
1: $1000\times\dfrac{40}{60} \approx 667\ \Omega$
2: $100\times\dfrac{87}{13} \approx 669\ \Omega$
3: $10\times\dfrac{98.5}{1.5} \approx 657\ \Omega$
4: $1\times\dfrac{99}{1} = 99\ \Omega$
Reading 4 does not agree with the others.
Solution by Sreeraj P, M.Sc Physics