Question

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.
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

Answer 1

Correct Answer - B::C
Refer Fig. 2 (EP).7.
For first student, `R_(2)=10Omega, R_(1)=5Omega, R_(3)=5Omega`
For other student, `R_(2)=1000Omega, R_(1)=500Omega, R_(3)=5Omega`
According to Wheatsone bridge principle
`(R_(2))/(R)=(R_(1))/(R_(3))` or `R=R_(3)xx(R_(2))/(R_(1))`
Putting values is above relation, we note that the value of R for both the students is `10Omega`.
The Wheatstone bridge is most sensitive and accurate if the resitance of al the four arms of bridge is of the same value. Therefore, the erros 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 large, the currents through the arms of bridge will be feeble. This will make the determination of null point accurately more difficult. Thus, option (b) and (c) are correct.