The Wheatstone Bridge and Balance
Bring the detector to 0
The figure is a bridge of four resistors joined in a diamond, and G in the middle is the detector that measures the voltage between the two midpoints. Change the standard resistor R_3 and the difference in potential between the left and right midpoints changes; the moment the two potentials become equal, the detector reads exactly 0. Find that balance point.
A bridge is two dividers face to face
A bridge is two voltage dividers placed side by side on the same source. The left divider (R_1 and R_2) sets a potential at midpoint A, and the right divider (R_3 and R_x) sets one at midpoint C. The detector looks at the voltage between the two midpoints A and C; if the two potentials differ, current flows through the detector, and if they are equal, none does.
Balance is when the opposing ratios match
The potential at midpoint A is proportional to R_2/(R_1+R_2), and the potential at midpoint C to R_x/(R_3+R_x). Setting the two equal and rearranging gives 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 in it. Even if the source wavers, the balance point stays put.
So it measures an unknown resistance precisely
Solving the balance condition for the unknown resistance gives R_x = R_3·(R_2/R_1). With a precisely known ratio R_2/R_1 and a standard resistor R_3 with an accurate dial, R_x can be read straight from the value of R_3 at the moment the detector reads 0. In this figure R_1 = 100 Ω and R_2 = 200 Ω, and the hidden R_x is 300 Ω, so the bridge balances at R_3 = 150 Ω. Because it catches the moment of 0 instead of measuring a magnitude, the method is not swayed by the meter's scale errors and is very precise.
Back to the first screen
As you changed the standard resistor, the detector voltage started with one sign, crossed 0, and passed to the opposite sign, and the point where it read exactly 0 was balance. At that moment R_1·R_x = R_2·R_3 held, so the unknown resistance could be read straight from the standard resistor's dial. The idea of catching the moment of 0 instead of measuring a value is what makes the bridge a tool for precise measurement.