In a Wheatstone bridge arrangement (P, Q, R and S), the resistors P and Q are nearly equal. The bridge is balanced when R = 500 Ω. On interchanging P and Q, the value of R for balancing is 505 Ω. The value of S will be:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 502.5 Ω
At balance the Wheatstone bridge condition is \( P/Q = R/S \). Write it for both settings:
\( \displaystyle \frac{P}{Q} = \frac{500}{S} \)
\( \displaystyle \frac{Q}{P} = \frac{505}{S} \)
Multiplying the two equations removes P and Q:
\( \displaystyle 1 = \frac{500 \times 505}{S^{2}} \)
\( \displaystyle S = \sqrt{500 \times 505}\,\Omega = \sqrt{252500}\,\Omega \approx 502.5\,\Omega \)
Shortcut: Since P and Q are nearly equal, the two balancing values lie symmetrically about S, so S is close to their average: \( (500 + 505)/2 = 502.5\,\Omega \).