The range of resistance measured in a Kelvin bridge is

Question

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Option B: $1\ \Omega$ to $10\ \mu\Omega$

Explanation & Concepts:
The Kelvin double bridge is a specialized variation of the Wheatstone bridge designed specifically for the precise measurement of very low resistances, typically ranging from $1\ \Omega$ down to $1\ \mu\Omega$. It eliminates the effects of lead and contact resistances by incorporating a secondary set of ratio arms.

Working Principle: The Kelvin double bridge introduces an auxiliary pair of 'inner' ratio arms to compensate for the resistance of the lead connecting the low-resistance standard and the unknown resistor. By establishing a potential balance between these inner arms and the outer arms, the error caused by contact resistance at the terminals is nullified, ensuring accurate measurement of values in the micro-ohm range.

Key Formulas: $R = \frac{P}{Q} S + \frac{qr}{p+q+r} (\frac{P}{Q} - \frac{p}{q})$ — Fundamental balance equation where terms denote ratio arms and lead resistance $r$; $R = \frac{P}{Q} S$ — Balanced condition when $\frac{P}{Q} = \frac{p}{q}$

Key Points: Used exclusively for low resistance measurements.; Eliminates lead and contact resistance errors.; Requires a sensitive galvanometer for null detection.; The bridge uses four terminals: two for current and two for potential.

Advantages: High accuracy for low resistance values.; Independent of contact resistance at current terminals.

Disadvantages: Complex circuit configuration.; Requires careful balancing of two sets of ratio arms.

Applications: Measurement of resistance of short copper wires.; Determination of low resistance in motor/generator windings.; Standardizing low-resistance shunts.

Additional Info: The range $1\ \Omega$ to $10\ \mu\Omega$ is the industry standard for Kelvin bridge classification.. Wheatstone bridge is typically used for resistances above $1\ \Omega$ to avoid error due to lead resistance.

Answer: B is correct — The Kelvin double bridge is specifically engineered for precision measurement of low resistances in the range of $1\ \Omega$ down to $10\ \mu\Omega$.

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

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Option A: $10\ \Omega$ to $10\ m\Omega$

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Option C: $0.01\ \Omega$ to $10\ M\Omega$

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Option D: $0.1\ \Omega$ to $10\ n\Omega$

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