The measurement of an unknown resistance R is to be carried out using Wheatstone bridge (see Fig. 2(EP).3). Two students perform an experiment in two way. The first student takes `R_(2)=10 Omega` and `R_(1)=5Omega`. The other student takes `R_(2)=1000Omega` and `R_(1)=500Omega`. In the standard arm, both take `R_(3)=5Omega`. Both find `R=(R_(2))/(R_(1))R_(3)=10Omega` within errors.

Options

A. The errors of measurnment of the two students are the same.
B. Errors of measurnment do depend on the accuracy with which `R_(2)` and `R_(1)` can be measured.
C. If the students uses larger 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 measurnment.

Answer

B, C

Explanation

Given, for first student,
`R_(2) = 10 Omega, R_(1) = 5 Omega, R_(3) = 5Omega`
For second student, `R_(1) = 500 Omega, R_(3)= 5 Omega`
Now, according to Wheatstone.s bridge rule,
`R_(2)/R = R_(1)/R_(3) rArr R = R_(3) xx R_(2)/R_(1)`

Now putting all the values in Eq. (i), we get `R= 10 Omega` for both students. Thus, we can analyse that the Wheatstone bridge is most sensitive and accurate if resistance are of same value.
Thus, the errors of measurnment of the two students depend on the accuracy and sensitivity of the brdge, which in turn depends on the accuracy with which `R_(2)` and `R_(1)` can be measured.
When `R_(2)` and `R_(1)` are larger, the currents through the arms of bridge is very weak. This can make the determination of null point accurately more difficult.