Wheatstone bridge behavior — when a Wheatstone bridge is exactly balanced, what is the output (bridge) voltage between the detector nodes?

Introduction / Context:
The Wheatstone bridge is a classic network used for precision measurement of resistance and for sensing with strain gauges, RTDs, and other transducers. The hallmark of a balanced bridge is a null (zero) indication at the detector. This question checks that fundamental behavior.

Given Data / Assumptions:

• Four resistive arms forming a diamond: R1/R2 in one leg, R3/Rx in the other (for example).
• Input (excitation) across one diagonal; detector across the other diagonal.
• Balanced condition satisfied (ratio R1/R2 = R3/Rx).

Concept / Approach:
At balance, the voltage division in each leg produces identical node potentials at the detector nodes. Since the detector nodes are at the same potential, their difference is zero. The bridge therefore exhibits 0 V across the output diagonal, allowing sensitive null detection and high-resolution measurement by observing deviations from zero when the bridge is slightly unbalanced.

Step-by-Step Solution:

Verification / Alternative check:
Real bridges use galvanometers or instrumentation amplifiers. At balance, the indicator reads zero; minute changes in Rx produce small differential voltages which can be amplified to infer the change precisely.

Why Other Options Are Wrong:

• Same as input / very high: Output is zero at balance, not full-scale or large.
• Dependent on unknown R: At balance, it is strictly zero regardless of the actual values so long as the ratio condition holds.

Common Pitfalls:
Confusing bridge balance with maximum sensitivity; maximum sensitivity occurs near but not exactly at null when using certain measurement strategies.

Final Answer:
Equal to 0 V — a balanced Wheatstone bridge has zero output.