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%