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Wheatstone Bridge Calculator

Check bridge balance and calculate unknown resistance from R₁/R₂ = R₃/R₄

Parameters

Ωⓘ
Ωⓘ
Ωⓘ
Ωⓘ
Show Trail

Controls

xⓘ

Calculated Values

R₁/R₂:
0.50;0.50;
R₃/R₄:
0.50;0.50;
R₄ for balance:
400.00;Ω400.00;Ω
Balanced (1=yes):
1.00;1.00;

Examples

Balanced bridge

100, 200, 200, 400 Ω.

  • Balanced (1=yes): 1.001.00

Find R₄ for balance

R₁=50, R₂=100, R₃=150 Ω.

  • R₄ for balance: 300.00300.00

Visualization

Wheatstone Bridge — Precision Resistance Measurement

A Wheatstone bridge has four resistors in a diamond: R₁ and R₂ on one branch, R₃ and R₄ on the other, with a galvanometer G between the midpoints and a battery across the outer nodes.

Balance condition: when the bridge is balanced, no current flows through G. Then potentials at the midpoints are equal, giving R₁/R₂ = R₃/R₄, or R₁R₄ = R₂R₃.

To find unknown R₄: R₄ = R₃R₂/R₁ when R₁, R₂, R₃ are known standards. Slight imbalance gives small G current — sensitive to tiny R changes.

Sensitivity is highest when all four arms have comparable resistance (ratio near 1). Used in strain gauges: tiny ΔR from deformation unbalances the bridge.

Kelvin double bridge extends the method for very low resistances (μΩ), eliminating lead-wire resistance errors.

AC bridges (e.g. Maxwell, Wien) measure capacitance and inductance using similar null-balance principles with AC excitation.

Key Concepts

  • Balance: R₁/R₂ = R₃/R₄
  • Unknown: R₄ = R₃R₂/R₁ at balance
  • Galvanometer current zero at null
  • Sensitive to small ΔR in one arm
  • Strain gauge: ΔR/R ~ strain ε
  • Kelvin bridge for low R measurement

Real-World Applications

  • Precision resistance standards in labs
  • Strain gauges and load cells
  • RTD temperature sensors (Pt100)
  • Moisture and pressure sensors
  • Class 12 meter bridge experiments

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Physics Equations

Balance:
R1R2=R3R4\frac{R_1}{R_2} = \frac{R_3}{R_4}
Unknown R₄:
R4=R3R2R1R_4 = \frac{R_3 R_2}{R_1}

Step-by-Step Solution

See how the main results are calculated.

1

Step 1: Label Bridge Arms

Assign R₁, R₂ on one branch; R₃, R₄ on the other; galvanometer between midpoints.

Explanation:

Balance means no potential difference between midpoints — no current through the galvanometer.

2

Step 2: Write Balance Condition

Equation:

R1R2=R3R4⇔R1R4=R2R3\frac{R_1}{R_2} = \frac{R_3}{R_4} \quad \Leftrightarrow \quad R_1 R_4 = R_2 R_3

Explanation:

Derived from equal midpoint potentials when G carries zero current.

3

Step 3: Evaluate Both Ratios

Calculation:

R1R2=100200=0.500000\frac{R_1}{R_2} = \frac{100}{200} = 0.500000 \\
R3R4=200400=0.500000\frac{R_3}{R_4} = \frac{200}{400} = 0.500000

Result:

Ratios are equal — bridge is BALANCED

Explanation:

Compare left and right ratios. Equality within measurement tolerance means null galvanometer.

4

Step 4: Balance Conclusion

State whether galvanometer current is zero.

Result:

IG=0(balanced)I_G = 0 (balanced)

Explanation:

No current through galvanometer; unknown resistance can be found from known arms.

5

Step 5: Solve for R₄ at Balance

Equation:

R4=R3R2R1R_4 = \frac{R_3 R_2}{R_1}

Calculation:

R4=200×200100=400.000000ΩR_4 = \frac{200 \times 200}{100} = 400.000000 \Omega

Result:

R4(forbalance)=400.000000ΩR₄ (for balance) = 400.000000 Ω

Explanation:

Given R₄ = 400 Ω, matches the balance value 400.0000 Ω.

6

Step 6: Cross-Multiplication Check

Equation:

R1R4=R2R3R_1 R_4 = R_2 R_3

Calculation:

R1R4=40000.0000,R2R3=40000.0000R_1 R_4 = 40000.0000, \quad R_2 R_3 = 40000.0000

Explanation:

Products should be equal at balance — alternative form avoids division by small R₂.

Frequently Asked Questions (FAQ)

Why use a bridge instead of a multimeter?

Null detection avoids meter loading errors and can resolve very small resistance changes with high precision.

What is a slide-wire bridge?

A variant using a uniform wire; balance position gives resistance ratio from wire lengths.

Can I use AC with a Wheatstone bridge?

Yes — AC bridges measure impedance; use AC galvanometer or headphones for null detection.

Why four resistors?

Ratio comparison cancels supply voltage fluctuations; only ratios matter at balance.

Temperature effect?

All arms should be at similar temperature, or use compensating dummy gauge in strain setups.

Practice MCQs

  1. At balance, current through the galvanometer is:
  2. If R₁=100 Ω, R₂=200 Ω, R₃=200 Ω, balance requires R₄ =
  3. Wheatstone bridge is best for measuring:
  4. Strain gauges use a bridge because:
  5. Balance condition can be written as:
  6. If bridge is NOT balanced, galvanometer shows:

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