Question

A balanced Wheatstone bridge ABCD has the following arm resistances:
$R_{AB} = 1 \text{k}\Omega \pm 2.1% ; R_{BC} = 100 \Omega \pm 0.5% ; R_{CD}$ is an unknown resistance; $R_{DA} = 300 \Omega \pm 0.4%$. The value of $R_{CD}$ and its accuracy is

• A. 30 Ω $\pm$ 3 Ω
• B. 30 Ω $\pm$ 0.9 Ω
• C. 3000 Ω $\pm$ 90 Ω
• D. 3000 Ω $\pm$ 3 Ω

Hint:

In a Wheatstone bridge, the value of the unknown resistance can be found using the balance condition. The accuracy of the measurement depends on the tolerances of the known resistances.

Answer 1

The Correct Option is A

Step 1: Wheatstone Bridge Balance Condition.
For a balanced Wheatstone bridge, the ratio of resistances in the arms must be equal. That is, \(\frac{R_{AB}}{R_{BC}} = \frac{R_{DA}}{R_{CD}}\). By using the given resistances and their tolerances, we can calculate the value of \(R_{CD}\).
Step 2: Analyzing the options.
- (A) 30 Ω $\pm$ 3 Ω: This matches the calculated value based on the resistances and their tolerances.
- (B) 30 Ω $\pm$ 0.9 Ω: This is also a reasonable estimate of \(R_{CD}\) based on the given data.
- (C) 3000 Ω $\pm$ 90 Ω: This is too large compared to the expected range for \(R_{CD}\).
- (D) 3000 Ω $\pm$ 3 Ω: This also does not match the expected range based on the calculations.
Step 3: Conclusion.
The correct answers are (A) and (B), as they both align with the expected value and accuracy for \(R_{CD}\).