Why Kelvin bridge is used for measurement of low resistance?

Question

Examoogle · Accepted Answer

The correct answer is Option C: Due to contact and lead resistance. The Kelvin bridge is specifically designed to measure low resistances (typically below 1 Ω) because, in such circuits, the resistance of the connecting leads and contacts becomes comparable to the unknown resistance itself. Standard bridges like the Wheatstone bridge introduce significant errors due to these lead resistances, which are minimized in the Kelvin bridge through a second set of ratio arms.

Step-by-Step Solution & Concepts:
The Kelvin bridge is specifically designed to measure low resistances (typically below 1 Ω) because, in such circuits, the resistance of the connecting leads and contacts becomes comparable to the unknown resistance itself. Standard bridges like the Wheatstone bridge introduce significant errors due to these lead resistances, which are minimized in the Kelvin bridge through a second set of ratio arms.

Working Principle: The Kelvin bridge uses an additional set of ratio arms, often called inner ratio arms, connected to the potential terminals of the unknown resistor. By providing a secondary path that makes the potential drop across the lead resistance negligible in the measurement, it ensures that the contact and lead resistance do not add to the measured value of the unknown resistance $R_x$.

Key Formulas: $R_x = \frac{P}{Q}S + \frac{rq}{p+q+r} (\frac{P}{Q} - \frac{p}{q})$; $R_x = \frac{P}{Q}S$ — Simplified Kelvin balance condition

Key Points: Used for measuring resistance values less than 1 ohm.; Eliminates lead resistance errors by using four-terminal resistance measurements.; Employs two sets of ratio arms to maintain a balanced condition.; Crucial in characterizing shunt resistors and busbar resistances.

Advantages: High accuracy for low resistance measurements.; Minimizes the effect of connecting lead resistance.; Utilizes null-detection principle for precision.

Disadvantages: Complex design compared to a standard Wheatstone bridge.; Requires four-terminal connection for the test resistor.

Applications: Calibration of low-value shunts.; Measurement of internal resistance of batteries.; Resistance of electrical machines and transformer windings.

Additional Info: The Wheatstone bridge fails for low resistance as lead resistance $(r_L)$ appears in series with the unknown $(R_x)$, making the measured value $(R_x + r_L)$ rather than $R_x$.. Option A is incorrect as the source EMF affects sensitivity, not the lead error compensation.. Option B is incorrect; while high current is used to improve signal-to-noise, it is a requirement for sensitivity, not the cause for using the bridge type.

Answer: C is correct — The Kelvin bridge is specifically designed to eliminate the parasitic errors introduced by lead and contact resistances which significantly distort low resistance measurements.

Exam Tip: Always remember: Wheatstone bridge is for medium resistance ($1\Omega$ to $100k\Omega$), whereas Kelvin bridge is the specialized tool for low resistance ($

Examoogle · Answer

Option A: Due to e.m.f source used

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Option B: Due to a large current flow

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Option D: Due to power dissipation across the circuit

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