Short Answer:

A Kelvin bridge is a modified form of the Wheatstone bridge used to accurately measure very low resistances, typically in the milliohm range. It eliminates the effect of lead and contact resistances by using a second set of voltage sensing connections, known as Kelvin connections.

This technique ensures that the measurement is not affected by the resistance of the connecting wires or contact points, which is especially important when the value of the resistance being measured is very small.

Detailed Explanation:

Kelvin bridge for low resistance measurement

When measuring very low resistance values (below 1 ohm), even a small error from connecting wires or contact points can lead to significant inaccuracies. Traditional methods like the Wheatstone bridge are not suitable in such cases because they include the resistance of leads and contacts in the measurement.

The Kelvin bridge, also called the double bridge, solves this problem by using an improved circuit design that separates the current path from the voltage sensing path, allowing only the actual resistance under test to influence the result.

Basic Concept and Working:

1. Two Sets of Connections:
   • The Kelvin bridge uses four terminals: two for passing current and two for measuring voltage.
   • The current flows through the outer terminals of the unknown resistor.
   • The voltage drop is measured across the inner terminals, avoiding voltage drop from wires.
2. Bridge Design:
   • The circuit is an extended version of the Wheatstone bridge, with an additional pair of resistors forming a second loop.
   • A galvanometer or sensitive voltmeter is used to detect balance.
3. Elimination of Lead Resistance:
   • Since the voltmeter is connected in a separate loop with negligible current, the resistance of connecting leads does not affect the measurement.
   • This ensures a true reading of only the unknown low resistance.
4. Balancing the Bridge:
   • The known standard resistors are adjusted until the galvanometer shows zero deflection.
   • At this balanced point, the unknown resistance can be calculated accurately using the known resistor values.

Mathematical Expression:

At bridge balance, the ratio of the known resistors equals the ratio in the other arm, and the unknown resistance RxR_xRx​ can be calculated without the effect of lead resistance:

R1R2=R3Rx⇒Rx=R2⋅R3R1\frac{R_1}{R_2} = \frac{R_3}{R_x} \Rightarrow R_x = \frac{R_2 \cdot R_3}{R_1}R2​R1​​=Rx​R3​​⇒Rx​=R1​R2​⋅R3​​

Where:

• RxR_xRx​ = Unknown low resistance
• R1,R2,R3R_1, R_2, R_3R1​,R2​,R3​ = Known resistors

Applications:

• Measuring contact resistance in electrical joints
• Testing transformer windings
• Measuring shunt resistors
• Used in metrology and calibration labs
• Evaluating battery connectors or relay contacts

Advantages:

• Highly accurate measurement of low resistance
• Eliminates error due to lead and contact resistance
• Suitable for precision testing and laboratory applications
• Ensures stable and repeatable readings

Conclusion:

A Kelvin bridge is specially designed to measure very low resistances accurately by using a four-terminal method that separates the current and voltage paths. This eliminates the effect of unwanted resistances from leads and contacts, which could otherwise distort the result. The Kelvin bridge is a reliable tool in precision electrical testing, especially where small resistance values must be measured without error.