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.

Answer

B, C

Explanation

For a balanced Wheatstone bridge:
`(R_(2))/(R_(1)) = (R )/(R_(2))`
`R= R_(3) (R_(2))/(R_(1))`

For the first student, measurement is performed using the below given values of known resistances:
`R_(1) =10Omega, R_(2) = 5Omega, R_(3) = 5Omega`
`rArr R= 10 Omega`
For the second student, measurement is performed using the below given values of known resistances:
`R_(2) = 1,000 Omega R_(1) = 500Omega R_(3) = 5 Omega`
`rArr R=10Omega`
Even through the value of R comes out to be same, the error of measurement will not be same. It will depend on the accuracy and sensitivity of a bridge, which further depends on the values of resistances `R_(1) and R_(2)` and how accurately these are measured, If resistance `R_(2) and R_(1)` are large, current through that branch will be feeble. This can make determination of null point difficult. So, option (b) and (c ) are correct.