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 l1 more accurately.
B. He should change S to 1000 Q and repeat the \ experiment.
C. He should change S to 3 Q and repeat the experiment
D. He should give up hope of a more accurate measurement with a meter bridge.

Explanation

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

### Step 1: Understanding the Meter Bridge Setup
In a meter bridge, two resistances are connected in a circuit. The unknown resistance \( R \) is placed in one gap, and a standard resistance \( S \) is placed in the other gap. The balance point (null point) is found by sliding a jockey along the bridge wire.

### Step 2: Using the Formula for Resistance
The relationship between the resistances and the balancing length is given by the formula:
\[ R = \frac{S \cdot L}{100 - L} \]
where \( L \) is the length from one end of the bridge wire to the null point.

### Step 3: Analyzing the Given Values
The student has chosen \( S = 100 \, \Omega \) and found the null point at \( L_1 = 2.9 \, \text{cm} \). We can substitute these values into the formula to find \( R \):
\[ R = \frac{100 \cdot 2.9}{100 - 2.9} = \frac{290}{97.1} \approx 2.99 \, \Omega \]

### Step 4: Improving Accuracy
To improve the accuracy of the measurement, the student is advised to change the standard resistance \( S \). By increasing \( S \) to \( 1000 \, \Omega \), the balancing length \( L \) will also increase, which allows for a more precise measurement of \( R \). This is because larger lengths reduce the relative error in measurement.

### Step 5: Conclusion
Thus, the best way to improve the accuracy of the measurement is to change the standard resistance \( S \) to \( 1000 \, \Omega \) and repeat the experiment.