Question

The resistance \( R = \frac{V}{I} \) where \( V = (200 \pm 5) \, \text{V} \) and \( I = (20 \pm 0.2) \, \text{A} \). The percentage error in the measurement of \( R \) is:

• A. 3.5%
• B. 7%
• C. 3%
• D. 5.5%

Answer 1

The Correct Option is A

Step 1: Express \( R \) in Terms of \( V \) and \( I \)

\[ R = \frac{V}{I} \]

Step 2: Calculate the Percentage Error Using Error Analysis

The relative error in \( R \) is given by:

\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]

Substitute the values:

\[ \frac{\Delta R}{R} = \frac{5}{200} + \frac{0.2}{20} \]

Step 3: Simplify the Expression

\[ \frac{\Delta R}{R} = \frac{5}{200} + \frac{0.2}{20} = \frac{5}{200} + \frac{2}{200} = \frac{7}{200} \]

Step 4: Calculate the Percentage Error

\[ \text{Percentage Error} = \frac{\Delta R}{R} \times 100 = \frac{7}{200} \times 100 = 3.5\% \]

So, the correct answer is: 3.5%