The source of error in a Wheatstone bridge is due to

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Limiting errors of the three known resistances

Explanation: The primary source of measurement error in a Wheatstone bridge circuit arises from the inherent limiting errors (or tolerance levels) associated with the three known resistances used in the bridge arms. Since the unknown resistance is calculated based on the balanced ratio of these three, any deviation in their nominal values directly propagates into the calculated value of the unknown resistance.

Working Principle: The Wheatstone bridge operates on the null-detector principle where $R_x = \frac{R_2 R_3}{R_1}$. Because each resistor $R_1, R_2, R_3$ has an associated tolerance (e.g., $\pm 0.1\%$), the resultant error in $R_x$ is the cumulative effect of these individual component uncertainties. Total relative error is approximately the sum of the relative errors of the three known resistors.

Key Formulas: $R_x = \frac{R_2 R_3}{R_1}$ — Balance condition for unknown resistance; $\frac{\Delta R_x}{R_x} = \frac{\Delta R_1}{R_1} + \frac{\Delta R_2}{R_2} + \frac{\Delta R_3}{R_3}$ — Relative limiting error propagation

Key Points: The Wheatstone bridge is a highly accurate null-deflection method.; Limiting errors refer to the guaranteed maximum deviation from the nominal value.; Sensitivity of the bridge depends on the galvanometer, but error originates from resistors.; Thermal EMF and contact resistance also contribute to errors, but component tolerance is the primary limiting factor.

Advantages: High accuracy for medium-range resistance measurements; Simple circuit configuration based on ratio arms

Disadvantages: Not suitable for very low resistance measurement due to lead/contact resistance; Not suitable for very high resistance measurement due to sensitivity issues

Applications: Precision resistance measurement in laboratories; Strain gauge instrumentation

Additional Info: The limiting error of the bridge is generally the summation of the errors of the three ratio-arm resistors.. Option A is incorrect because the galvanometer affects sensitivity, not the static error of the bridge balance.. Option B affects noise levels, not the basic resistance balance accuracy.. Option D is the ideal state and is not a source of error.

Answer: C is correct — The accuracy of the bridge is constrained by the manufacturing tolerance of the three known resistors in the ratio arms.

Exam Tip: Always remember that in bridge circuits, component tolerance (limiting error) is a multiplicative factor in the final result, whereas thermal noise is an additive factor.

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