Question:
In a Wheatstone bridge, the bridge is balanced when the ratio of the resistances in the four arms satisfies
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[width=0.5\linewidth]{108.png}
In a Wheatstone bridge, the bridge is balanced when the ratio of the resistances in the four arms satisfies
[H]
[width=0.5\linewidth]{108.png}
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Remember that in a balanced Wheatstone bridge, the product of the resistances on one pair of opposite arms is equal to the product of the resistances on the other pair.
Updated On: May 31, 2026
- $P/Q = R/S$
- $P/R = S/Q$
- $PS = QR$
- $P+Q = R+S$
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The Wheatstone bridge is a circuit used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, making the current through the detector null. When the bridge is balanced, the ratio of resistances in opposite arms are equal.
Step 2: Meaning
In a balanced Wheatstone bridge, the potential difference across the mid-point of one pair of opposite arms is zero, indicating that no current flows through the galvanometer.
Step 3: Analysis
Consider a Wheatstone bridge with four resistors \(P\), \(Q\), \(R\), and \(S\) connected in such a way that they form two pairs of opposite arms. The bridge is balanced when the potential difference between points A and B (the mid-points of the opposite arms) becomes zero, meaning no current flows through the galvanometer. For the bridge to be balanced, the following condition must hold: \[\frac{P}{Q} = \frac{R}{S}\] This can be rearranged to: \[PS = QR\] Option A: \(P/Q = R/S\) is directly derived from the balance condition of the Wheatstone bridge. Option B: \(P/R = S/Q\) does not represent the correct ratio for a balanced bridge. Option C: \(PS = QR\) is mathematically equivalent to the condition derived from balancing the bridge, but it is not in the form given in Option A. Option D: \(P+Q = R+S\) does not have any direct relation with the balance condition of the Wheatstone bridge.
Step 4: Conclusion
The correct condition for a balanced Wheatstone bridge is that the ratio of resistances in opposite arms must be equal, which can be expressed as: \[\frac{P}{Q} = \frac{R}{S}\] Final Answer: (A)
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