Ncert Exercises & Solutions

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 \(R_2=10~\Omega\) 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 \(R = \dfrac{R_{2}}{R_{1}} R_{3} = 10 ~ \Omega \) 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 the determination of the null point accurately more difficult.
(d)	Wheatstone bridge is a very accurate instrument and has no errors of measurement.

Choose the correct option:
1. (a, c)
2. (c, d)
3. (b, c)
4. (c, d)

\begin{array}{l} (3) Hint : Use the concept of Wheatstone bridge . \\ Given, for first student, R_{2} = 10 Ω, R_{1} = 5 Ω, R_{3} = 5 Ω \\ For second student, R_{1} = 500 Ω R_{3} = 5 Ω \end{array}

Step 1: Find the value of R for both students.

Now, according to the Wheatstone bridge rule;

\frac{R_{2}}{R} = \frac{R_{1}}{R_{3}} \Rightarrow R = R_{3} \times \frac{R_{2}}{R_{1}}

.............(i)

Now putting all the values in Eq. (i), we get R = 10

Ω

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

R_{2}

and

R_{1}

can be measured.

When

R_{1} and R_{2}

, 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.

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