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CR · DC analysis

The Wheatstone Bridge and Balance

Catching the instant when two voltages become equal is far more precise than measuring a voltage directly. Learn the balance principle of the bridge, which uses four resistors to make that instant and measure an unknown resistance.

Tune the detector to zero

Slide the standard resistor R_3 and watch the voltage on the central detector. The instant the left and right midpoints reach the same potential, the detector reads exactly zero. Find that balance point.

Standard resistor R_3R_3 = 60 Ω
Detector voltage and reading
V_d = -1.67 V · R_x = 120 Ω
Unbalanced

A bridge is two dividers face to face

A bridge is two voltage dividers wired side by side across the same source. The left divider (R_1 and R_2) sets a potential at midpoint A; the right divider (R_3 and R_x) sets one at midpoint C. The detector sees the voltage between the two midpoints A and C. If the two potentials differ, current flows through the detector; if they are equal, none does.

Balance is when the opposing ratios match

The potential at A is proportional to R_2/(R_1+R_2), and at C to R_x/(R_3+R_x). Set them equal and it tidies up to R_1/R_2 = R_3/R_x, that is R_1·R_x = R_2·R_3. This single line — equal cross-products — is the balance condition, and remarkably the source voltage appears nowhere. Even if the supply drifts, the balance point stays put.

So it measures an unknown resistance precisely

Solving the balance condition for the unknown gives R_x = R_3·(R_2/R_1). With a precisely known ratio R_2/R_1 and an accurately calibrated standard resistor R_3, you read R_x straight off the value of R_3 at the moment the detector hits zero. Because you catch a null rather than measure an absolute value, you are not at the mercy of a meter’s scale error — so it is very precise.

ObserveVd = VA − VC
The detector is the difference of the two midpoints.
ChooseR1·Rx = R2·R3 → Vd = ?
At balance the detector is zero.
Fill inR1R2 = ?
The two opposing ratios are equal.
On your ownRx = R3 ?
Multiply the standard by the ratio.

Back to the first screen

As you slid the standard resistor, the detector voltage started on one side, crossed zero, and went over to the opposite sign, and the point reading exactly zero was the balance. At that instant R_1·R_x = R_2·R_3 held, so you could read the unknown straight from the standard’s dial. The idea of catching a null instead of measuring a value is what makes the bridge a tool of precise measurement.

A Wheatstone bridge joins four resistors in a diamond with a detector between the two midpoints. The balance condition is when the opposing ratios match, R1/R2 = R3/Rx (R1·Rx = R2·R3), and then the detector voltage is zero. Balance is independent of the source voltage. The unknown is Rx = R3·(R2/R1), measured precisely by catching the null.