## Wheatstone bridge

The Wheatstone bridge is used in two ways: (1) to measure the value of an unknown resistor by comparison to standard resistors, and (2) to detect small changes in a resistance transducer (e.g. thermistor).

For the first application, one needs a calibrated variable resistance (R4), two fixed known resistors (e.g. R1 and R2), and the unknown resistance (R3). In this simulation, R4 consists of the series combination of a fixed resistance and a variable resistance (to make fine adjustments possible). R4 is adjusted until the detector voltage is exactly zero, at which point R3/R4=R1/R2. Usually, R1 is made equal to R2, so R3 = R4 at balance.

For the second application, R3 is the resistive transducer. The bridge is initially balanced to "zero the baseline", then any changes in the transducer's resistance (R3) are detected by recording the detector voltage as it varies from zero.

You can change any of the resistances. Just click on the resistor value with the mouse pointer and edit like any text field. The slider on the right controls only the variable resistor component of R4.

The Wheatstone bridge is easily thought of as two voltage dividers. One voltage divider is formed of R1 and R3 and the other is formed of R2 and R4. The battery voltage serves as the input to the two voltage dividers, and their outputs (the junction of the two resistors) are connected together with the detector (a voltage-measuring device, assumed to have very high input resistance).

The output voltage of the first voltage divider is Vb R3 / (R1 + R3) and the output voltage of the second voltage divider is Vb R4 / (R2 + R4). When these two voltages are equal, the detector voltage is xero, and we say that the bridge is balanced. This happens when

Vb R3 / (R1 + R3) = Vb R4 / (R2 + R4)
or, cancelling out Vb, when
R3 / (R1 + R3) = R4 / (R2 + R4)