Question

In a Wheatstone bridge (see fig.), 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 :

• A. 402.5 ohm
• B. 401.5 ohm
• C. 403.5 ohm
• D. 404.5 ohm

Hint:

Write the balance condition for both arrangements, \(\frac{P}{Q} = \frac{400}{X}\) and \(\frac{Q}{P} = \frac{405}{X}\), and multiply them to eliminate \(P/Q\).

Answer 1

The Correct Option is A

In the figure P is in arm AB, Q in BC, R in AD and X in DC. Balance condition: \(\frac{P}{Q} = \frac{R}{X}\).
First case: \(\frac{P}{Q} = \frac{400}{X}\).
After interchanging P and Q: \(\frac{Q}{P} = \frac{405}{X}\).
Multiplying: \(1 = \frac{400\times 405}{X^2} \Rightarrow X = \sqrt{400\times 405} = \sqrt{162000}\approx 402.5\ \Omega\).
Answer: (1) 402.5 ohm