In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown

Q: Why do the first three readings give slightly different values for X?

In any real experiment, factors like end resistances of the copper strips, slight non-uniformity in the wire's cross-section, and human error in reading the scale cause slight variations. This is exactly why we take multiple readings and average them out.

Q: Why is the fourth reading so drastically wrong?

When the balancing length is very small, like 1 cm, the end resistance of the copper connecting strips becomes comparable to the resistance of that tiny 1 cm wire segment. This causes a massive percentage error, rendering the reading useless.

Q: What is the ideal balancing length in a meter bridge?

The ideal balancing length is between 40 cm and 60 cm. Operating near the center of the wire minimizes the percentage error in the measurement of length and significantly reduces the impact of end resistances.

Q: Can we interchange the known resistance R and the unknown resistance X?

Yes, interchanging them will simply change the balancing length from $l$ to $100 - l$. The calculated value of the unknown resistance will remain exactly the same.

Q: What happens if the galvanometer and battery are interchanged in the circuit?

The balance point remains completely unaffected. This is a fundamental property of the Wheatstone bridge network; the battery and galvanometer arms are conjugate to each other.

Question

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure
$\begin{array}{|c|c|c|}
\hline
	ext{S. No.} & R (\Omega) & l (	ext{cm}) \
\hline
1. & 1000 & 60 \
2. & 100 & 13 \
3. & 10 & 1.5 \
4. & 1 & 1.0 \
\hline
\end{array}$
Which of the readings is inconsistent?

Options:

(A) 3

(B) 2

(C) 1

(D) 4

Sigma Percentile · Accepted Answer

### Identifying the Inconsistent Reading in a Meter Bridge Experiment

The meter bridge is a practical application of the Wheatstone bridge principle, widely used to measure an unknown resistance with high precision. In this problem, we are presented with an observation table containing four sets of readings for a known resistance $R$ and the corresponding balancing length $l$. Our goal is to identify which of these readings is inconsistent with the rest.

### The Master Equation

For a balanced meter bridge, the ratio of the resistances in the two gaps is equal to the ratio of the lengths of the wire segments on either side of the null point. Mathematically, this is expressed as:

$$X = \left(\frac{100 - l}{l}ight) R$$

Here, $X$ is the unknown resistance, $R$ is the known resistance from the resistance box, and $l$ is the balancing length measured from the end adjacent to $R$. Since the unknown resistance $X$ is a physical wire that remains unchanged throughout the experiment, its calculated value should be approximately the same across all valid observations.

### Analyzing the Observations

Let's calculate the value of $X$ for each of the four cases provided in the table.

**Case 1:**
Given $R = 1000\ \Omega$ and $l = 60\ 	ext{cm}$.

$$X_1 = \left(\frac{100 - 60}{60}ight) 	imes 1000 = \frac{40}{60} 	imes 1000 = \frac{2000}{3} \approx 667\ \Omega$$

**Case 2:**
Given $R = 100\ \Omega$ and $l = 13\ 	ext{cm}$.

$$X_2 = \left(\frac{100 - 13}{13}ight) 	imes 100 = \frac{87}{13} 	imes 100 = \frac{8700}{13} \approx 669\ \Omega$$

**Case 3:**
Given $R = 10\ \Omega$ and $l = 1.5\ 	ext{cm}$.

$$X_3 = \left(\frac{100 - 1.5}{1.5}ight) 	imes 10 = \frac{98.5}{1.5} 	imes 10 = \frac{9850}{15} \approx 656\ \Omega$$

**Case 4:**
Given $R = 1\ \Omega$ and $l = 1.0\ 	ext{cm}$.

$$X_4 = \left(\frac{100 - 1}{1}ight) 	imes 1 = \frac{99}{1} 	imes 1 = 99\ \Omega$$

### Conclusion

Comparing the calculated values, we see that $X_1$, $X_2$, and $X_3$ all yield a result in the vicinity of $660\ \Omega$. However, $X_4$ gives a drastically different value of $99\ \Omega$. This massive deviation indicates that the fourth reading is highly inconsistent with the actual physical setup.

**Practical Insight:** In a real meter bridge experiment, readings taken very close to the ends of the wire (like $l = 1.0\ 	ext{cm}$) are highly inaccurate. At these extremes, the end resistances of the thick copper strips become comparable to the resistance of the short wire segment, leading to massive percentage errors. For the most accurate results, the known resistance $R$ should be chosen such that the null point lies near the middle of the wire ($l \approx 50\ 	ext{cm}$).

Select Answer:

Visualized Solution

Balanced Condition of Meter Bridge

Setup for Case 1

Calculation for Case 1

Setup for Case 2

Calculation for Case 2

Setup for Case 3

Calculation for Case 3

Setup for Case 4

Calculation for Case 4

Conclusion

The Way Forward

The Sigma Insight: Measuring Instruments

Identifying the Inconsistent Reading in a Meter Bridge Experiment

The Master Equation

Analyzing the Observations

Conclusion

Similar Questions

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