Bridges: Wheatstone, Kelvin and Schering With easy examples.

A bridge is a circuit that measures an unknown electrical quantity by balancing it against known standards until a detector reads zero. At balance, no current flows through the detector, so the result does not depend on the supply voltage or on the detector's calibration — only on the ratio of the known components. This "null method" is why bridges are among the most accurate ways to measure resistance, capacitance and inductance.

Different bridges solve different problems. The Wheatstone bridge measures medium resistances from about 1 Ω to a few megohms. The Kelvin double bridge measures very small resistances — cable joints, current shunts — where lead resistance would swamp a Wheatstone reading. The Schering bridge measures capacitance and the dielectric loss of insulators at AC, which matters for high-voltage equipment.

Key Concepts

• Null detector: a sensitive galvanometer for DC bridges, or headphones/an amplifier for AC bridges, showing when balance is reached.
• Balance condition: the detector reads zero when the impedance ratios of adjacent arms are equal.
• Wheatstone bridge: four resistive arms with the unknown in one arm; the workhorse for medium resistance.
• Kelvin double bridge: adds a second set of ratio arms so that lead and contact resistance cancel out of the balance equation.
• Schering bridge: an AC bridge using a standard (loss-free) capacitor; it must balance both magnitude and phase.
• Dissipation factor (tan δ): measures how lossy a dielectric is; a rising tan δ in transformer or cable insulation warns of moisture and ageing.

Formulas

• Wheatstone balance: R1/R2 = R3/R4, so Rx = (R2 × R3) / R1, where Rx is the unknown arm and the others are the known arms in the standard diamond layout.
• Kelvin double bridge: Rx = (R2/R1) × Rs, where Rs is the standard low resistance — lead resistance cancels at balance.
• Schering bridge: Cx = C2 × (R4/R3) and tan δ = 2 × π × f × C4 × R4, where C2 is the standard capacitor and C4 the balancing capacitor.

Assumptions: DC bridges need steady, thermoelectric-free connections; AC bridges need a pure sine-wave source and shielding from stray electric and magnetic fields.

Worked Example

1. Wheatstone bridge arms: R1 = 100 Ω, R2 = 200 Ω, R3 = 150 Ω, unknown Rx in the fourth arm; the galvanometer reads zero.
2. At balance, R1/R2 = R3/Rx, so Rx = (R2 × R3) / R1.
3. Rx = (200 × 150) / 100 = 300 Ω.
4. If Rx drifted by just 1 Ω, the galvanometer would deflect — the bridge resolves fractions of a percent with ordinary resistors.

Common Misconceptions

• "The supply voltage must be precisely known." At null balance no current flows in the detector regardless of the supply voltage; even an unsteady battery gives the right answer.
• "Wheatstone works for any resistance." Below about 1 Ω, lead and contact resistances corrupt the result — that is exactly the problem the Kelvin double bridge was invented to fix.
• "AC bridges balance like DC ones." An AC bridge must satisfy both magnitude and phase balance, so two adjustments (R4 and C4 in the Schering bridge) are needed, done alternately until both are right.

Real-World Applications

• Measuring RTD temperature sensors in industrial process control.
• Locating cable faults by loop testing with a Wheatstone bridge.
• Factory testing of capacitors and high-voltage insulation with the Schering bridge.
• Strain-gauge force and pressure measurement (a Wheatstone bridge of four gauges).

Bridges turn measurement into comparison: balance the unknown against a standard until a detector reads zero. Wheatstone for everyday resistance, Kelvin for milliohms, Schering for capacitors and insulation health.