The measurement of an unknown resistance R is to be carried out using a Wheatstone bridge. Two students perfor

Question

The measurement of an unknown resistance R is to be carried out using a Wheatstone bridge. Two students perform an experiment in two ways. The first student takes R₂ = 10 Ω and R₁ = 5 Ω. The other student takes R₂ = 1000 Ω and R₁ = 500 Ω. In the standard arm, both take R₃ = 5 Ω. Both find R = (R₂/R₁) × R₃ = 10 Ω within errors. Consider the following statements:
(a) The errors of measurement of the two students are the same.
(b) Errors of measurement do depend on the accuracy with which R₂ and R₁ can be measured.
(c) If the student uses large values of R₂ and R₁, the currents through the arms will be feeble. This will make the determination of the null point accurately more difficult.
(d) Wheatstone Bridge is a very accurate instrument and has no errors of measurement.

Choose the correct option from the given ones:

Accepted Answer

The accuracy and sensitivity of a Wheatstone bridge depend on the components and the current.
1. **Dependence on Accuracy (Statement b):** The result $R = R_3 rac{R_2}{R_1}$ depends directly on the values of $R_1, R_2,$ and $R_3$. Any error in measuring these known resistances will propagate to the result. Thus, errors depend on the accuracy of $R_1$ and $R_2$.
2. **Sensitivity and Current (Statement c):** For the second student, using large resistances ($1000 \Omega, 500 \Omega$) significantly increases the total resistance of the circuit. According to Ohm's law ($I = V/R$), this reduces the current flowing through the arms. A smaller current leads to a smaller deflection in the galvanometer near the null point, making it difficult to detect the exact balance point accurately. This lack of sensitivity increases experimental error.

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