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 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

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 wheatstone bridge rule,
`(R_(2))/(R)=(R_(1))/(R_(3))impliesR=R_(3)xx(R_(2))/(R_(1))`
Now putting all the values inn Eq. (i) we get `R=10Omega` for both student. thus, we can analyse that the wheatstone bridge is most sensitive and accurate if resistance are of same value. thus, the errors of measurement of the two studets depend on te 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,t he currents though the arms of bridge is very weak. This can make the determination of null point accurately more difficult.