The measurement of an unknown resistance R is to be carried out using a Wheatstone bridge. Two students perform an experiment in two ways. The first students take R2 = 10 Ω and R1 =5 Ω. The other student takes R2 =1000 Ω and R1 =500 Ω. In the standard arm, both take R3 = 5 Ω.

Both find R=R2R1R3=10 Ω 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 R2 and R1 can be measured.

(c) If the student uses large values of R2 and R1, the currents through the arms will be feeble. This will make the determination of the null point accurately more difficult.

(d) Wheatstone bridge is a very accurate instrument and has no errors of
measurement.

1. (a, c)

2. (c, d)

3. (b, c)

4. (c, d)

(3) Hint: Use the concept of Wheatstone bridge.Given,for first studentR2=10Ω, R1=5Ω, R3=5ΩFor second studentR1=500Ω R3=5Ω
Step 1: Find the value of R for both students.
Now, according to the Wheatstone bridge rule;
R2R=R1R3R=R3×R2R1 .............(i)
                                 
Now putting all the values in Eq. (i), we get R = 10Ω for both students. Thus, we can analyze that the Wheatstone bridge is most sensitive and accurate if resistances are of the same value.
Thus, the errors of measurement of the two students depend on the accuracy and sensitivity of the bridge, which in turn depends on the accuracy with which R2 and R1 can be measured.
When R1 and R2, are larger, the currents through the arms of the bridge are very weak. This can make the determination of the null point accurately more difficult.