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 measurement of 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. Whatstone bridge is a very accurate instrument and has no errors of measurement.

Answer

B, C

Explanation

Given, for first student, `R_(2)=10Omega,R_(1)=5Omega,R_(3)=5Omega`
For second student, `R_(1)=500Omega,R_(3)=5Omega`.

Now, according to whatstone bridge rule,
`(R_(2))/(R)=(R_(1))/(R_(3))impliesR=R_(3)xx(R_(2))/(R_(1))`
Now putting all the values in Eq. (i) we get `R=10Omega` for both students. Thus, we can analyse that the wheatstone bridge is mot sensitive and accurate if resistances are of same value.
Thus, the errors of measurement of the two students depend on the accuracy and sensitivity of the bridge, which inturn 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.