The measurement of an unknown resistance R is to be carried...

The measurement of an unknown resistance $R$ is to be carried out using Wheatstones bridge. Two students perform an experiment in two ways. The first students takes $R_{2}=10 \Omega$ and $R_{1}=5 \Omega$. The other student takes $R_{2}=1000 \Omega$ and $R_{1}=500 \Omega$. In the standard arm, both take $R_{3}=5 \Omega$. Both find $\begin{aligned} R &=\frac{R_{2}}{R_{1}} R_{3}=10 \Omega \text { within errors. } \\ \text { [NCERT Exemplar] } \end{aligned}$ (a) The errors of measurement of the two students are the same (b) Errors of measurement do depend on the accuracy with which $R_{2}$ and $R_{1}$ can be measured (c) If the student uses large values of $R_{2}$ and $R_{1}$, the currents through the arms will be feeble. This will make determination of null point accurately more difficult (d) Wheatstone bridge is a very accurate instrument and has no errors of measurement

The measurement of an unknown resistance $R$ is to be carried out using Wheatstones bridge. Two students perform an experiment in two ways. The first students takes $R_{2}=10 \Omega$ and $R_{1}=5 \Omega$. The other student takes $R_{2}=1000 \Omega$ and $R_{1}=500 \Omega$. In the standard arm, both take $R_{3}=5 \Omega$. Both find $\begin{aligned} R &=\frac{R_{2}}{R_{1}} R_{3}=10 \Omega \text { within errors. } \\ \text { [NCERT Exemplar] } \end{aligned}$
(a) The errors of measurement of the two students are the same
(b) Errors of measurement do depend on the accuracy with which $R_{2}$ and $R_{1}$ can be measured
(c) If the student uses large values of $R_{2}$ and $R_{1}$, the currents through the arms will be feeble. This will make determination of null point accurately more difficult
(d) Wheatstone bridge is a very accurate instrument and has no errors of measurement

Key Concepts

Wheatstone Bridge Principle

The Wheatstone bridge is an electrical circuit used to measure an unknown resistance by balancing two legs of a bridge circuit. When the bridge is balanced (i.e., no voltage difference is detected between its midpoints), the ratio of the resistances in one branch equals the ratio in the other, allowing the unknown resistance to be calculated accurately in terms of known resistances.

Error Propagation in Ratio Measurements

In resistance measurements using the Wheatstone bridge, the accuracy of the result depends on the precision of the known resistors used in the ratio. Errors in measuring these resistances directly affect the calculated value of the unknown resistance since the result is determined by the ratio of two measured values. Therefore, precise calibration and measurement of these resistors are crucial for minimizing overall measurement errors.

Impact of Absolute Resistance Values on Bridge Performance

The choice of absolute resistance values in the arms of a Wheatstone bridge can influence the measurement sensitivity and accuracy. Using larger resistance values can lead to lower currents in the bridge circuit, which may make the detection of the null (zero-current point) more challenging. This difficulty in accurately finding the balance point introduces additional measurement uncertainty.

Limitations of Measurement Instruments

While the Wheatstone bridge is a highly effective instrument for precise resistance measurements, it is still subject to limitations such as component tolerances, measurement errors, and environmental influences. Even though it is designed to reduce certain types of systematic error, the instrument does not completely eliminate errors in measurement, and its accuracy is contingent upon the quality and calibration of the components used.

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