A resistance R is to be measured using a meter bridge. Student chooses the standared 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 folllowing is a useful way?

Options

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

Explanation

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

### Step 1: Understand the Meter Bridge Principle
The meter bridge operates on the principle of Wheatstone bridge. The balance condition is given by:

\[ \frac{R}{S} = \frac{l_1}{100 - l_1} \]

where \( R \) is the unknown resistance, \( S \) is the standard resistance, and \( l_1 \) is the length from one end of the bridge to the null point.

### Step 2: Substitute Known Values
Given that \( S = 100 \, \Omega \) and \( l_1 = 2.9 \, \text{cm} \), we can substitute these values into the equation:

\[ \frac{R}{100} = \frac{2.9}{100 - 2.9} = \frac{2.9}{97.1} \]

### Step 3: Calculate the Value of \( R \)
From the equation, we can express \( R \):

\[ R = 100 \times \frac{2.9}{97.1} \]

Calculating this gives:

\[ R \approx 2.99 \, \Omega \]

### Step 4: Analyze the Error
To improve accuracy, we need to minimize the percentage error in the measurement of \( R \). The percentage error is minimized when the lengths \( l_1 \) and \( 100 - l_1 \) are as close to each other as possible.

### Step 5: Adjust the Standard Resistance \( S \)
Since \( l_1 = 2.9 \, \text{cm} \) is much closer to 0 than to 100 cm, this indicates that \( R \) is much smaller than \( S \). To achieve a more accurate measurement, we should choose a smaller value for \( S \) so that the null point is closer to the midpoint (50 cm).

### Step 6: Choose an Appropriate Value for \( S \)
To make the ratio \( \frac{R}{S} \) closer to \( 1:1 \), we should reduce \( S \) significantly. Based on the analysis, reducing \( S \) to around \( 3 \, \Omega \) would allow the null point to be closer to the middle of the bridge.

### Conclusion
Thus, the best way to improve accuracy is to change \( S \) to \( 3 \, \Omega \) and repeat the experiment.

### Final Answer
The correct option is: **He should change \( S \) to \( 3 \, \Omega \) and repeat the experiment.**

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