The resistant R=V/I where `V=100+-0.5V` and `I=10+-0.2A`. The percentage error in V is 5% and in I is 2%. Find the total percentage error is R.

Explanation

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

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

Where:
- \( V = 100 \, \text{V} \) with an uncertainty of \( \pm 0.5 \, \text{V} \)
- \( I = 10 \, \text{A} \) with an uncertainty of \( \pm 0.2 \, \text{A} \)

### Step 1: Calculate the percentage error in \( V \)
The percentage error in \( V \) is given as:

\[ \text{Percentage error in } V = \frac{\Delta V}{V} \times 100 = \frac{0.5}{100} \times 100 = 0.5\% \]

### Step 2: Calculate the percentage error in \( I \)
The percentage error in \( I \) is given as:

\[ \text{Percentage error in } I = \frac{\Delta I}{I} \times 100 = \frac{0.2}{10} \times 100 = 2\% \]

### Step 3: Combine the percentage errors
The total percentage error in \( R \) can be calculated by adding the percentage errors of \( V \) and \( I \):

\[ \text{Total percentage error in } R = \text{Percentage error in } V + \text{Percentage error in } I \]

Substituting the values we found:

\[ \text{Total percentage error in } R = 5\% + 2\% = 7\% \]

### Conclusion
Thus, the total percentage error in the resistance \( R \) is:

\[ \text{Total percentage error in } R = \pm 7\% \]

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