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

Explanation

To find the percentage error in the resistance \( R \) given by the formula \( R = \frac{V}{I} \), where \( V = (100 \pm 5.0) \, V \) and \( I = (10 \pm 0.2) \, A \), we will follow these steps:

### Step 1: Identify the values and uncertainties
- Voltage \( V = 100 \, V \) with an uncertainty \( \Delta V = 5.0 \, V \)
- Current \( I = 10 \, A \) with an uncertainty \( \Delta I = 0.2 \, A \)

### Step 2: Calculate the relative uncertainties
The relative uncertainty in \( V \) is given by:
\[ \frac{\Delta V}{V} = \frac{5.0}{100} = 0.05 \]

The relative uncertainty in \( I \) is given by:
\[ \frac{\Delta I}{I} = \frac{0.2}{10} = 0.02 \]

### Step 3: Use the formula for the relative uncertainty in \( R \)
The formula for the relative uncertainty in \( R \) when \( R = \frac{V}{I} \) is:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]

### Step 4: Substitute the values
Substituting the relative uncertainties we calculated:
\[ \frac{\Delta R}{R} = 0.05 + 0.02 = 0.07 \]

### Step 5: Convert to percentage error
To find the percentage error in \( R \), we multiply the relative uncertainty by 100:
\[ \text{Percentage Error} = \frac{\Delta R}{R} \times 100 = 0.07 \times 100 = 7\% \]

### Final Answer
The percentage error in the resistance \( R \) is \( 7\% \).

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