Tricky Circuit

The Wheatstone bridge

Notice a tiny resistance imbalance

A Wheatstone bridge compares two voltage dividers, each made from two resistors. Balance means their middle voltages are equal, so their difference is zero. Vs is supply voltage and Rs the chosen sensor resistance. mV means millivolt: 1 mV = 0.001 V.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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How it works

Three fixed 1000 Ω resistors and one chosen 800–1200 Ω resistance. Midpoint readings are unloaded: the meter draws no current. No amplifier, real strain measurement, heating or resistor errors are modeled.

Left divider: Vleft = Vs/2. Right divider: Vright = Vs × Rs/(1000 + Rs). Display the signed difference Vright − Vleft in millivolts. Increasing the lower-right resistance raises its midpoint.

Difficulty

  1. Build · Observe

    Power on at Vs = 5 V and Rs = 1000 Ω. Both midpoints are 2.5 V; difference 0 mV.

    Need a hint?

    Vs=5 V; Rs=1000 Ω → 2.5 V; 2.5 V; 0 mV

  2. Explore · Explore

    Keep 5 V; choose Rs = 1100 Ω. Right midpoint ≈ 2.61905 V, difference ≈ +119.0476 mV.

    Need a hint?

    Vs=5 V; Rs=1100 Ω → Vright≈2.61905 V; ΔV≈+119.0476 mV

  3. Solve it · Solve

    Keep 5 V; choose Rs = 900 Ω. Right midpoint ≈ 2.36842 V, difference ≈ −131.5789 mV.

    Need a hint?

    Vs=5 V; Rs=900 Ω → Vright≈2.36842 V; ΔV≈−131.5789 mV

Extra reading and circuit recipes

The Wheatstone bridge

A strain gauge is a resistive sensor whose resistance changes when it is stretched or compressed; strain means relative change in length. A bridge can reveal that small change. Here you choose resistance directly: no force, weight or deformation is measured or calibrated.

Vleft = Vs/2; Vright = Vs × Rs/(1000 + Rs); ΔV = (Vright − Vleft) × 1000 mV

The reference divider gives a comparison level. With Rs = 1000 Ω the ratios match; away from balance the signed difference tells which midpoint is higher. Real measurement needs suitable sensing and calibration.

A useful connection

Balanced does not mean zero midpoint voltage: here both sides sit at half the supply.

Beyond the model

Equal resistance changes above and below 1000 Ω do not give equal-size voltages; the divider relation is nonlinear.

A useful trap to avoid

Use right minus left consistently. Swapping meter leads changes the sign. A larger supply scales both voltages and their difference; it does not by itself improve accuracy.

Both sides are 2.5 V. Their difference is…

  1. 0 mV
  2. 2.5 V
  3. 5 V
Read more

A bridge measures the difference of its two midpoints, not one midpoint relative to ground.

Find balance

Choose supply 5 V and resistance 1000 Ω.

Both midpoints 2.5 V; difference 0 mV.

Below balance

Choose supply 5 V and resistance 900 Ω.

Right minus left ≈ −131.5789 mV.

Try another change

At Rs = 1100 Ω compare supplies 1 V and 5 V. The difference changes from about +23.8095 to +119.0476 mV, fivefold.

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