The resistance of a metal is given by `R = V//I` , where `V` is potential difference and `I` is current . In a circuit , the potential difference across resistance is `V = ( 8 +- 0.5) V` and current in resistance , `I = ( 4 +- 0.2)A`. What is the value of resistance with its percentage error?

Options

A. `( 2 +- 5.6%) Omega`
B. `( 2 +- 0.7%) Omega`
C. `( 2 +- 35%) Omega`
D. `( 2 +- 11.25%) Omega`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Calculate the Resistance
The formula for resistance \( R \) is given by:
\[ R = \frac{V}{I} \]
Where:
- \( V = 8 \, \text{V} \)
- \( I = 4 \, \text{A} \)

Substituting the values:
\[ R = \frac{8 \, \text{V}}{4 \, \text{A}} = 2 \, \Omega \]

### Step 2: Calculate the Absolute Errors
The absolute errors in the measurements are given as:
- \( \Delta V = 0.5 \, \text{V} \)
- \( \Delta I = 0.2 \, \text{A} \)

### Step 3: Calculate the Percentage Errors
The percentage error in \( V \) and \( I \) can be calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{\Delta V}{V} \times 100 \right) + \left( \frac{\Delta I}{I} \times 100 \right) \]

Calculating the percentage error for \( V \):
\[ \text{Percentage Error in } V = \frac{0.5}{8} \times 100 = 6.25\% \]

Calculating the percentage error for \( I \):
\[ \text{Percentage Error in } I = \frac{0.2}{4} \times 100 = 5\% \]

### Step 4: Combine the Percentage Errors
The total percentage error in resistance \( R \) is the sum of the percentage errors in \( V \) and \( I \):
\[ \text{Total Percentage Error} = 6.25\% + 5\% = 11.25\% \]

### Step 5: Write the Final Result
The value of resistance with its percentage error can be expressed as:
\[ R = 2 \, \Omega \pm 11.25\% \]

### Final Answer
The resistance is \( 2 \, \Omega \) with a percentage error of \( 11.25\% \).

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