A Wheatstone bridge is an electrical circuit used to precisely measure an unknown resistance by balancing two legs of a bridge circuit.
Lecture Video
Basic Diagram:
R1 R2
[–––]——A——[–––]
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R3 Rx (Unknown)
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GND GND
- A: Bridge output point (connected to a galvanometer)
- R1, R2, R3: Known resistances
- Rx: Unknown resistance
- Galvanometer detects current between nodes A and B
Principle:
- The bridge is balanced when:
- At balance, no current flows through the galvanometer.
Formula to find unknown resistance:
Applications:
- Measurement of unknown resistances
- Calibration of measuring instruments
- Temperature sensing (using thermistors or RTDs in the bridge)
Advantages:
- High accuracy
- Simple and reliable
- Widely used in sensor circuits (strain gauges, RTDs)
Here are 5 example problems based on the Wheatstone Bridge principle with solutions:
Problem 1: Basic Resistance Measurement
Given: R₁ = 100 Ω, R₂ = 200 Ω, R₃ = 150 Ω, Rx = unknown. Bridge is balanced. Find Rx.
Solution: At balance:
Problem 2: Bridge Not Balanced
Given: R₁ = 100 Ω, R₂ = 100 Ω, R₃ = 100 Ω, Rx = 200 Ω. Question: Is the bridge balanced?
Solution: Check ratio:
Not equal → Bridge is not balanced
Problem 3: Unknown Resistance Using Galvanometer Reading
Given: R₁ = 120 Ω, R₂ = 80 Ω, R₃ = 150 Ω, galvanometer shows zero current (balanced). Find Rx.
Solution:
Problem 4: Ratio Setup
Given: R₁ = 60 Ω, R₂ = 30 Ω. Bridge is balanced and Rx = 90 Ω. Find R₃.
Solution:
Problem 5: Voltage across galvanometer
Given: R₁ = R₂ = 100 Ω, R₃ = Rx = 200 Ω. Battery = 10V. Find voltage across galvanometer.
Solution:
When the Wheatstone bridge is balanced, the voltage across the galvanometer is 0 V.
Why?
In a Wheatstone bridge:
- One diagonal is connected to a voltage source (say, across A and C).
- The other diagonal (B–D) is where the galvanometer is connected.
When the bridge is balanced:
Then, the potential at point B (between R₁ and R₂) is equal to the potential at point D (between R₃ and Rₓ).
Hence, the potential difference V_{BD} = 0, so the galvanometer shows zero current and voltage across it is 0 V.
Working Model
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Worksheets
