Kelvin Double Bridge: Definition, Working Principle, Formula & Applications

The Kelvin Bridge, also known as the Thompson Bridge, is used to measure unknown resistances with values less than 1Ω. It is a modified version of the Wheatstone Bridge, designed specifically for accurate low-resistance measurements. One of the most precise methods for measuring low resistance is the Kelvin Double Bridge. This bridge is an advanced version of the Wheatstone bridge, specifically designed to eliminate errors due to contact and lead resistances. The Wheatstone bridge is capable of measuring resistances ranging from a few ohms to several kilo-ohms. However, it tends to produce errors when used to measure low resistances. To address this issue, the Wheatstone bridge has been modified into what is known as the Kelvin bridge. The Kelvin bridge is specifically designed for accurately measuring low resistances.

What is Kelvin Double Bridge?

A kelvin double bridge is a modified Wheatstone bridge circuit used specifically to measure very low resistances that are typically less than 0.1 ohms. It is called a "double bridge" because it contains two separate sets of ratio arms to eliminate errors from lead and contact resistances that plague normal Wheatstone bridge measurements at low values. By incorporating an additional set of ratio arms connected to a central measurement point, the kelvin double bridge enables obtaining precise resistance readings free from such error-inducing external resistances. This makes it an essential tool in applications where accurate measurement of low resistance is required, such as in cable resistance measurement, transformer winding resistance, and other similar scenarios.

The Wheatstone Bridge is typically used to measure resistances ranging from a few ohms to several kilo-ohms. However, it becomes prone to errors when measuring low resistances. To overcome this limitation, the Wheatstone Bridge was modified into the Kelvin Bridge, which is specifically designed for accurate low-resistance measurements.

Kelvin Double Bridge Working Principle

Consider a standard Wheatstone bridge circuit used to measure an unknown resistance R using a standard resistance S. The contact resistance r between R and S introduces measurement errors. In the kelvin double bridge, a second set of ratio arms p and q is added such that the ratio p/q equals the main arms ratio P/Q. A galvanometer is connected between p and q arms at a point that divides r into two equal parts r1 and r2. This ensures that r causes no net error in the final resistance calculation.

Fig-Circuit Diagram of Kelvin Double Bridge

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Derivation/ Equation for Finding Unknown Resistance Value

The ratio arms P and Q are used to connect the galvanometer at the optimal point between junctions j and k. These junctions j and k help minimize the impact of connecting leads. P and Q represents the first set of ratio arms, while p and q represent the second set of ratio arms in the bridge circuit. The galvanometer is connected between the arms p and q at point d. Point d is positioned at the center of the resistance r between points mmm and n to eliminate the effect of the connecting lead resistance, which lies between the unknown resistance R and the standard resistance S.

The ratio p/q is adjusted to be equal to P/Q. When the bridge is balanced, no current flows through the galvanometer. At this balanced condition, the potential difference between points a and b is equal to the voltage drop between points E and m.

Now,

For zero deflection of galvanometer …

As we know, P/Q = p/q then above equation becomes

The equation above represents the working principle of the Kelvin Bridge. It demonstrates that the results obtained from the Kelvin Double Bridge are unaffected by the connecting lead resistance. To achieve accurate results, it is important that the ratios of the bridge arms are equal. Any inequality in the arm ratios can introduce errors in the measurement. Additionally, the value of the resistance r should be kept as low as possible to ensure precise results.

Kelvin Double Bridge Formula:

Thermoelectric EMF may be induced in the bridge during the measurement process. This effect can be minimized by taking readings with the battery connections reversed. The true resistance value is then determined by averaging the two measurements.

Difference between Kelvin Bridge and Kelvin Double Bridge

The Kelvin Bridge and Kelvin Double Bridge are both electrical bridge circuits used to measure very low resistance with high precision. While they are closely related, they differ in configuration and application to minimize measurement errors. Here are the differences between Kelvin Bridge and the Kelvin Double Bridge:

Feature	Kelvin Bridge	Kelvin Double Bridge
Basic Principle	Modified Wheatstone bridge	Enhanced Kelvin bridge with additional ratio arms
Measurement Range	Low resistance (milliohm level)	Very low resistance (micro-ohm to milliohm level)
Accuracy	High	Very High
Error Compensation	Compensates for lead and contact resistances	Better compensation, even for varying parasitic resistances
Number of Ratio Arms	One pair	Two pairs (main and auxiliary ratio arms)
Complexity	Relatively simple	More complex due to additional components
Voltage Measurement Terminals	Two separate terminals from current path	Same concept, but with extra components for fine adjustment
Application Areas	General lab use, wire resistance, conductor testing	Industrial and precise research use, bus bars, shunt testing
Cost and Setup	Lower cost, easier setup	Higher cost, more intricate setup

Kelvin Double Bridge Advantages and Disadvantages

Here is a detailed breakdown of the Kelvin Double Bridge advantages and disadvantages, often used for precision low-resistance measurements:

Advantages of Kelvin Bridge

• Provides error-free measurement of very low resistances <1 ohm.
• Measurement is independent of contact resistance between test leads and resistor.
• Simpler compared to other low-resistance measurement methods.
• High sensitivity and precision due to the ratiometric measurement principle.

Disadvantages of Kelvin Bridge

• Requires precision resistors to maintain ratio accuracy.
• The setup is more complex than a simple Wheatstone bridge.
• Not suitable for industrial applications due to the involvement of ratios.
• Measurements are time-consuming due to multiple adjustments.

Kelvin Double Bridge Applications

Kelvin Double Bridge Applications are explained below:

• Measurement of very low resistances (micro-ohm to milliohm range)
• Calibration of low-resistance standard resistors
• Resistance testing of conductors such as wires, cables, and busbars
• Measurement of transformer and motor winding resistance
• Accurate assessment of contact resistances in connectors, relays, and switches
• Testing shunt resistors used in precision current measurement (e.g., in ammeters)
• Resistance measurement of power system components (circuit breakers, grounding connections, isolators)
• Use in research and metrology laboratories for high-precision electrical measurements

Conclusion

The kelvin double bridge serves as a basic method for electrical engineers to precisely measure ultra-low resistances. Its self-compensating design effectively removes external resistance error sources, thus enabling applications like resistance thermometry.

This article concludes all the information related to the Kelvin double bridge, which helps to propel your preparation for various AE/JE examinations. To boost your preparation, you should test yourself through a series of Mock Tests for Electrical Engineering Exams. You can check the syllabus for the AE/JE exam. You can visit the Testbook app to keep yourself updated with all the exam-oriented information related to the upcoming examinations, including GATE Electrical, SSC JE, ESE, RRB JE, and state AE/JE Electrical exam.