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)=2.9cm`. He is told to attempt to improve the accuracy. Which of the following is a useful way?

Options

A. He should measure `l_(1)` more accurately
B. He should change S to `1000Omega` and repeat the experiment
C. He should change S to 3`Omega` and repeat the experiment
D. He should given up hope of a more accurate measurement with a meter bridge

Answer

To solve the problem of measuring resistance \( R \) using a meter bridge, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Meter Bridge Principle**: The meter bridge operates on the principle of Wheatstone bridge. When the bridge is balanced, the ratio of the lengths on either side of the bridge is equal to the ratio of the resistances.

2. **Set Up the Equation**: Given that the standard resistance \( S = 100 \, \Omega \) and the null point is found at \( l_1 = 2.9 \, \text{cm} \), we can use the formula:
\[ \frac{l_1}{S - l_1} = \frac{R}{S} \]
where \( S \) is the standard resistance.

3. **Substitute the Known Values**: Plugging in the values we have:
\[ \frac{2.9}{100 - 2.9} = \frac{R}{100} \]

4. **Calculate the Length Difference**: Calculate \( 100 - 2.9 = 97.1 \, \text{cm} \).

5. **Set Up the Equation**: Now we can rewrite the equation:
\[ \frac{2.9}{97.1} = \frac{R}{100} \]

6. **Cross Multiply**: Cross multiplying gives:
\[ 2.9 \cdot 100 = R \cdot 97.1 \]

7. **Calculate \( R \)**: Now, solving for \( R \):
\[ R = \frac{2.9 \cdot 100}{97.1} \]
\[ R \approx 2.99 \, \Omega \]

8. **Determine the Accuracy Improvement**: To improve the accuracy of the measurement, it is beneficial to use a standard resistance \( S \) that is closer to the value of \( R \). Since \( R \approx 3 \, \Omega \), using a standard resistance of \( 3 \, \Omega \) will provide a more accurate measurement.

### Conclusion:
Thus, the useful way to improve the accuracy is to choose a standard resistance \( S \) that is equal to \( 3 \, \Omega \).