Question

A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be $100\Omega$. He finds the null point at $l_1=2.9$cm. He is told to attempt to improve the accuracy. Which of the following is a useful way?

• A. He should measure $l_1$ more accurately
• B. He should change S to $1000\Omega$ and repeat the experiment
• C. He should change S to $3\Omega$ and repeat the experiment
• D. He should give up hope of a more accurate measurement with a meter bridge

Answer 1

The correct option is C He should change S to $3\Omega$ and repeat the experiment

$\text{Given:}$

${\ell }_1=2.9cm,S=100\Omega$

$\text{Step 1: When the metre bridge is balanced at length}{\ell }_1$

$\frac{{\ell }_1}{100-{\ell }_1}=\frac{R}{S}$

$\Rightarrow \frac{2.9}{100-2.9}=\frac{R}{100}$

$\Rightarrow R=2.98\Omega =3\Omega$

$\text{Step 2: Improving the accuracy}$

To improve the accuracy in measurement, the null point should be found near the middle of the meter bridge wire, i.e. both the known and unknown resistance should be nearly equal.

$\therefore \frac{R}{S}=\frac{1}{1}$

$\Rightarrow S=R=3\Omega$

Therefore, the student should change $S$ to $3\Omega$ and repeat the experiment.

Hence, Option(C) is correct.