Balanced Wheatstone bridge computation: In a balanced bridge, RV = 3,500 Ω, R2 = 200 Ω, and R3 = 680 Ω. What is the value of the unknown resistor RUNK that satisfies the balance condition?

Introduction / Context:
The Wheatstone bridge is a precision measurement circuit. Under balance (zero detector current), the ratio of resistances in one leg equals the ratio in the opposite leg. Using this condition, we can compute the unknown resistance from the three known arms without needing the supply voltage or detector characteristics.

Given Data / Assumptions:

• Bridge is balanced (detector at null).
• RV = 3,500 Ω (variable arm set to this value).
• R2 = 200 Ω, R3 = 680 Ω.
• RUNK is the unknown arm opposite RV in the standard ratio relation.

Concept / Approach:
For a balanced Wheatstone bridge: R_unknown / R2 = RV / R3 (equivalently R_unknown = R2 * RV / R3), depending on arm labeling. This relation arises from equal voltage division in both legs leading to zero potential difference across the detector.

Step-by-Step Solution:

Verification / Alternative check:
Check the ratios: RV / R3 ≈ 3500 / 680 ≈ 5.147; RUNK / R2 ≈ 1029 / 200 ≈ 5.145. These are effectively equal, confirming bridge balance within rounding.

Why Other Options Are Wrong:

• 680 Ω, 200 Ω, 880 Ω: Do not satisfy the required ratio equality when paired with the given arms.

Common Pitfalls:

• Missetting the ratio (e.g., inverting R2/R3).
• Rounding too early and losing precision in the final answer.

Final Answer:
1,029 Ω