Q 12-03-269JEE MainJEE Main 2019 (11 Jan, Shift 1)Medium
In a Wheatstone bridge (see figure), resistances $P$ and $Q$ are approximately equal. When $R = 400\ \Omega$, the bridge is balanced. On interchanging $P$ and $Q$, the value of $R$, for balance, is $405\ \Omega$. The value of $X$ is close to
Answer: (D) $402.5\ \Omega$
Balance condition: $\dfrac PQ = \dfrac RX$.
First balance: $\dfrac PQ = \dfrac{400}{X}$. After interchanging: $\dfrac QP = \dfrac{405}{X}$.
Multiplying the two equations:
$$1 = \frac{400\times405}{X^2} \Rightarrow X = \sqrt{162000} \approx 402.5\ \Omega$$
Solution by Sreeraj P, M.Sc Physics