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.
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.