Wheatstone bridge property at balance: if a Wheatstone bridge is balanced, what is the voltage between the midpoints A and B relative to the source voltage VS?

Introduction / Context:
The Wheatstone bridge is a classic four-resistor network used for precise measurement and sensing. A key concept is the “balance” condition, where the ratio of resistances in one branch equals the ratio in the other. This question checks your recall of the bridge’s null property at balance.

Given Data / Assumptions:

• Standard Wheatstone topology: two series legs in parallel across a source VS.
• Node A is the junction of the upper and lower resistors in the left leg; node B is the junction in the right leg.
• “Balanced” means R1/R2 = R3/R4, using a consistent top-to-bottom or bottom-to-top ratio convention.
• Assume ideal meters with infinite input resistance (no loading).

Concept / Approach:
At balance, the potential divider in the left leg produces the same fraction of source voltage as the right leg. Therefore, the potentials at nodes A and B are equal, making the bridge (detector) voltage VAB = VA − VB equal to zero. This is the basis for using a null detector: the galvanometer reads zero at balance.

Step-by-Step Solution:

Verification / Alternative check:
If the bridge is slightly unbalanced, VAB is small but nonzero; its polarity indicates which ratio is greater. Exactly at balance, the null meter reads zero even though current flows in the legs.

Why Other Options Are Wrong:
VAB equals VS: impossible since VA and VB are internal divider tap voltages.
VAB equals VS/2: only in a special, incidental case and not a balance criterion.
“Thevenin voltage of the source”: irrelevant—the null depends on the resistor ratios, not on source reduction.
“Undefined without load”: the detector is assumed high impedance; VAB is well-defined.

Common Pitfalls:
Reversing resistor labeling and ratio orientation; assuming “no current flows anywhere” at balance—current still flows in the legs, but not through the detector.

Final Answer:
VAB equals 0 (nodes at equal potential)