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In a balanced Wheatstone bridge, if the position of detector and source are interchanged, the bridge will still remain balanced. This inference can be drawn from
- a)Reciprocity theorem
- b)Duality theorem
- c)Compensation theorem
- d)Equivalence theorem
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a balanced Wheatstone bridge, if the position of detector and sourc...
Reciprocity Theorem:
- It states that In any branch of a network or circuit, the current due to a single source of voltage (V) in the network is equal to the current through that branch in which the source was originally placed when the source is again put in the branch in which the current was originally obtained.
- This theorem is used in the bilateral linear network which consists of bilateral components.
- In simple words, we can state the reciprocity theorem as when the places of voltage and current source in any network are interchanged the amount or magnitude of current and voltage flowing in the circuit remains the same.
The location of the voltage source and the current source may be interchanged without a change in current. However, the polarity of the voltage source should be identical to the direction of the branch current in each position.
In a balanced Wheatstone bridge, if the position of detector and source are interchanged, the bridge will still remain balanced. This inference is drawn from the Reciprocity theorem.
In a balanced Wheatstone bridge, if the position of detector and source are interchanged, the bridge will still remain balanced. This inference is drawn from the Reciprocity theorem.
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In a balanced Wheatstone bridge, if the position of detector and sourc...
Understanding the Wheatstone Bridge
A Wheatstone bridge is a circuit used to measure unknown resistances by balancing two legs of a circuit. It consists of four resistors, a voltage source, and a galvanometer (detector). When balanced, the voltage across the galvanometer is zero.
Concept of Balance
In a balanced Wheatstone bridge, the ratio of the resistances in one leg is equal to the ratio in the other leg. This balance can be expressed as:
- R1/R2 = R3/R4
Where R1, R2, R3, and R4 are the resistances in the respective arms of the bridge.
Reciprocity Theorem
The assertion that interchanging the positions of the detector and the source does not affect the balance of the Wheatstone bridge is derived from the reciprocity theorem. This theorem states that:
- The response in a network due to a given source (voltage or current) remains the same if the locations of the source and detector are interchanged.
Implications of the Theorem
- When the source and detector are swapped, the conditions for balance are preserved.
- Since the ratios of resistance remain unchanged, the bridge remains balanced, ensuring that the current through the galvanometer remains zero.
Conclusion
Thus, the ability of the Wheatstone bridge to maintain balance regardless of the position of the detector and source can be conclusively attributed to the reciprocity theorem. This fundamental principle is essential in circuit analysis and design, especially in applications involving precise measurements of resistance.
A Wheatstone bridge is a circuit used to measure unknown resistances by balancing two legs of a circuit. It consists of four resistors, a voltage source, and a galvanometer (detector). When balanced, the voltage across the galvanometer is zero.
Concept of Balance
In a balanced Wheatstone bridge, the ratio of the resistances in one leg is equal to the ratio in the other leg. This balance can be expressed as:
- R1/R2 = R3/R4
Where R1, R2, R3, and R4 are the resistances in the respective arms of the bridge.
Reciprocity Theorem
The assertion that interchanging the positions of the detector and the source does not affect the balance of the Wheatstone bridge is derived from the reciprocity theorem. This theorem states that:
- The response in a network due to a given source (voltage or current) remains the same if the locations of the source and detector are interchanged.
Implications of the Theorem
- When the source and detector are swapped, the conditions for balance are preserved.
- Since the ratios of resistance remain unchanged, the bridge remains balanced, ensuring that the current through the galvanometer remains zero.
Conclusion
Thus, the ability of the Wheatstone bridge to maintain balance regardless of the position of the detector and source can be conclusively attributed to the reciprocity theorem. This fundamental principle is essential in circuit analysis and design, especially in applications involving precise measurements of resistance.
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In a balanced Wheatstone bridge, if the position of detector and source are interchanged, the bridge will still remain balanced. This inference can be drawn froma)Reciprocity theoremb)Duality theoremc)Compensation theoremd)Equivalence theoremCorrect answer is option 'A'. Can you explain this answer?
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