Question

The measurement of an unknown resistance R is to be carried out using Wheatstones bridge (figure). Two students perform an experiment in two ways. The first students takes 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 = `R_2/R_1 R_3` = 10 Ω within errors.

1. The errors of measurement of the two students are the same.
2. Errors of measurement do depend on the accuracy with which R₂ and R₁ can be measured.
3. If the student uses large values of R₂ and R₁, the currents through the arms will be feeble. This will make determination of null point accurately more difficult.
4. Wheatstone bridge is a very accurate instrument and has no errors of measurement.

Options

• a and b

• b and c

• c and d

• a and d

Answer 1

b and c

Explanation:

Wheatstone bridge: The bridge is an arrangement of four resistance which can be used to measure one of them in terms of rest. Here arms AB and BC are called ratio arm and arms AC and BD are called conjugate arms.

Balanced bridge: The bridge is said to be balanced when deflection in the galvanometer is zero, i.e. no current flows through the galvanometer or in other words V_B = V_D. In the balanced condition `P/Q = R/S`, on mutually changing the position of cell and galvanometer this condition will not change.

Unbalanced bridge: If the bridge is not balanced current will flow from D to B if V_D > V_B, i.e. (V_A – V_D) < (V_A – V_B) which gives PS > RQ.

According to the problem for first students, R₂ = 10 Ω, R₁ = 5 Ω, R₃ = 5 Ω

For second student, R₁ = 500 Ω, R₂ = 1000 Ω, R₃ = 5 Ω

Let us take R₄ = R.

Now, according to the Wheatstone bridge rule,

`R_2/R_1 = R_4/R_3` ⇒ `R_4 = R_3 xx R_2/R_1`

Now putting all the values in above equation, we get R = 10 Ω for both students. Thus, we can analyse 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.

The currents through the arms of bridge is very weak when R₂ and R₁ are larger.

This can make the determination of null point accurately more difficult.