The measurement of an unknown resistance R is to be carried out using Wheatstone bridge as given in the figure below. Two students perform an experiment in two ways. The first students takes `R_(2) = 10 Omega and R_(1) = 5 Omega`. The other student takes `R_(2) = 1000 Omega and R_(1) = 500 Omega`. In the standard arm, both take `R_(3) = 5 Omega` . both find R = `(R_(2))/(R_(1)) , R_(3) = 10 Omega` 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 accwately more difficult
D. Wheatstone bridge is a very accurate instrument and has no errors of measurement.

Explanation

(B, C )

For balanced condition of Wheatstone bridge,
`(R_(2))/(R) = (R_(1))/(R_(3)) `
`therefore R = R_(3) xx (R_(2))/(R_(1))`
For first student : `R_(1) = 5 Omega , R_(2) = 10 Omega` and
`R_(3) = 5 Omega`
`therefore R = 5 xx (10)/(5) = 10 Omega`
For second student : `R_(1) = 500 Omega , R_(2) = 1000 Omega`,
`" " R_(3) = 5 Omega`
`therefore R = 5 xx (1000)/(500) = 10 Omega`
If` R_(1) and R_(2)` are chosen in such a way that it is of very large then current flowing through galvanometer will be very small hence null point can be obtained accurately.