A Wheatstone bridge is a four-resistor circuit used to measure an unknown resistance or detect very small resistance changes. Its diamond shape makes it easy to compare two voltage dividers at once. When the bridge is balanced, the middle detector reads zero volts, which gives a precise resistance relationship.
This matters in engineering because tiny changes in resistance can represent force, pressure, temperature, or strain.
Understanding Engineering: The Wheatstone Bridge
The supply is connected across one diagonal of the bridge. The measuring instrument is connected across the other diagonal. Current travels through the two outer branches, and each branch sets a midpoint voltage.
The instrument compares these midpoint voltages rather than trying to measure one resistor by itself. This comparison is useful because a stable shared supply change affects both sides in a similar way.
Much of that unwanted change cancels in the comparison. A sensitive instrument can then focus on the small difference caused by the component being tested.
A bridge is especially sensitive near its balanced setting. If one resistance changes slightly, one midpoint voltage moves while the reference midpoint stays nearly fixed. The output begins at zero and grows in one direction for an increase in resistance.
It grows in the opposite direction for a decrease. For very small changes, the output is often approximately proportional to the resistance change.
Engineers choose resistor values carefully because the supply voltage, resistor sizes, and sensor resistance determine how large this output becomes. A larger output is easier to measure, but too much supply voltage can heat a sensor and change its resistance by accident.
Strain gauges show why this circuit is widely used. A strain gauge is a thin metal pattern bonded to an object such as a beam, a weighing platform, or a machine part. When the object stretches, the pattern becomes slightly longer and thinner.
Its resistance rises by a tiny amount. When the object is compressed, its resistance usually falls. A bridge can use one gauge, two gauges, or four gauges.
Using matched gauges in several arms increases the signal. It can reduce errors from temperature changes because nearby gauges warm or cool by similar amounts. Load cells in digital scales, pressure sensors, and structural test equipment use this idea.
When learning the bridge, draw the circuit and label the four arms before doing any calculation. Identify which two resistors form the left branch and which form the right branch. Then find each midpoint voltage from the same reference point before subtracting them.
The subtraction order matters because it sets the sign of the output. Check units carefully. Resistance is measured in ohms, voltage in volts, and current in amperes.
Real measurements are limited by resistor tolerance, wire resistance, instrument input resistance, electrical noise, and temperature drift. A bridge may be theoretically balanced yet show a small reading in practice. Engineers often trim one resistor, average repeated readings, or use an amplifier to obtain a reliable result.
Key Facts
- Balance condition: R1/R2 = R3/R4
- For an unknown resistor Rx in place of R4: Rx = R3 R2/R1 when balanced
- Detector voltage: Vout = Vleft - Vright
- Voltage divider rule: Vnode = Vs Rbottom/(Rtop + Rbottom)
- At balance, Vout = 0 V and no current flows through the galvanometer or voltmeter.
- A strain gauge changes resistance by a small amount, and the bridge converts that change into a measurable voltage.
Vocabulary
- Wheatstone bridge
- A circuit of four resistive arms used to compare resistances by measuring the voltage between two middle nodes.
- Balance condition
- The resistance ratio condition that makes the two middle node voltages equal and the detector voltage zero.
- Galvanometer
- A sensitive meter used to detect very small currents, often used to show whether a bridge is balanced.
- Voltage divider
- A pair of series resistors that splits a supply voltage in proportion to their resistance values.
- Strain gauge
- A sensor whose electrical resistance changes slightly when it is stretched or compressed.
Common Mistakes to Avoid
- Using R1 + R2 = R3 + R4 as the balance rule. This is wrong because the bridge balances by equal voltage ratios, not by equal total resistance in the two sides.
- Assuming the detector always carries current. At balance, the two middle nodes are at the same voltage, so an ideal detector has zero voltage across it and no current through it.
- Mixing up the top and bottom resistors in the voltage divider formula. The node voltage depends on the resistor between the node and the reference point, so choosing the wrong resistor gives the wrong polarity or value.
- Treating a strain gauge resistance change as large. Strain gauges usually change by a very small fraction, so the bridge output is often in millivolts and may require amplification.
Practice Questions
- 1 A Wheatstone bridge is balanced with R1 = 120 ohms, R2 = 240 ohms, and R3 = 150 ohms. If the unknown resistor is R4, find R4.
- 2 A bridge has Vs = 10 V, R1 = 100 ohms, R2 = 100 ohms, R3 = 100 ohms, and R4 = 101 ohms. Using Vleft = Vs R2/(R1 + R2) and Vright = Vs R4/(R3 + R4), find Vout = Vleft - Vright.
- 3 A strain gauge in one arm of a balanced bridge is stretched so its resistance increases slightly. Explain why the bridge output is no longer zero and why this helps measure mechanical strain.