The resistance `R= (V)/(I)`, where `V= (100+-5.0) V` and `I=(10+-0.2)A`. Find the percentage error in `R`.

Options

A. `0.7%`
B. `0.5%`
C. `5%`
D. `7%`

Explanation

To find the percentage error in resistance \( R \), we start with the formula for resistance:

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

where \( V = 100 \pm 5.0 \, \text{V} \) and \( I = 10 \pm 0.2 \, \text{A} \).

### Step 1: Identify the uncertainties
- The uncertainty in voltage \( \Delta V = 5.0 \, \text{V} \)
- The uncertainty in current \( \Delta I = 0.2 \, \text{A} \)

### Step 2: Calculate the relative errors
The relative error in \( V \) is given by:

\[ \frac{\Delta V}{V} = \frac{5.0}{100} = 0.05 \]

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

\[ \frac{\Delta I}{I} = \frac{0.2}{10} = 0.02 \]

### Step 3: Combine the relative errors
The total relative error in \( R \) can be calculated using the formula:

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

Substituting the values we calculated:

\[ \frac{\Delta R}{R} = 0.05 + 0.02 = 0.07 \]

### Step 4: Convert to percentage error
To find the percentage error, we multiply the relative error by 100:

\[ \text{Percentage error in } R = 0.07 \times 100 = 7\% \]

### Final Result
The percentage error in resistance \( R \) is \( \pm 7\% \).

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