Question

The measurement of an unknown resistance 𝑅 is to be carried out using Wheatstone bridge. Two students perform an experiment in two ways. The first student 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 $R=\frac{R_2}{R_1}{R}_3=10\Omega$ within errors.

• A. 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.
  
• B. Errors of measurement do depend on the accuracy with which $R_2$ and $R_1$ can be measured.
  
• C. Wheatstone bridge is a very accurate instrument and has no errors of measurement
  
• D. The errors of measurement of the two students are the same.
  
• E. (b) and (c) above.

Answer 1

The correct option is E (b) and (c) above.

Error in the measurement of 𝑅

$\frac{\Delta R}{R}=\frac{\Delta R_2}{R_2}+\frac{\Delta R_1}{R_1}+\frac{\Delta R_3}{R_3}$

So, errors of measurement do depend on the accuracy with which $R_2$ and $R_1$ can be measured

If the student uses large values of $R_2$and $R_1$, the currents through the arms will be feeble and it will not be measured accurately, and it will also depend on the least count value of measuring instrument. So, this will make determination of null point accurately more difficult.

Final Answer: (𝑏), (𝑐)