The resistance of metal is given by `V = IR`, The voltage in the resistance is `V = (8 pm 0.5)V` and current in the resistance is `I = (2 +- 0.2)A`, the value fo resistance with its percentage error is

Options

A. `4 +- 16.25 %`
B. `4 +- 6.25 %`
C. `4 +- 10 %`
D. `4 +- 8 %`

Answer

To find the resistance \( R \) and its percentage error given the voltage \( V \) and current \( I \), we will follow these steps:

### Step 1: Write down the formula for resistance
The resistance \( R \) is given by Ohm's law:
\[ R = \frac{V}{I} \]

### Step 2: Substitute the values of voltage and current
We have:
- Voltage \( V = 8 \pm 0.5 \, V \)
- Current \( I = 2 \pm 0.2 \, A \)

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

### Step 3: Calculate the percentage error in resistance
To find the percentage error in \( R \), we use the formula for error propagation:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]
Where:
- \( \Delta V = 0.5 \, V \)
- \( V = 8 \, V \)
- \( \Delta I = 0.2 \, A \)
- \( I = 2 \, A \)

Substituting the values:
\[ \frac{\Delta R}{R} = \frac{0.5}{8} + \frac{0.2}{2} \]

Calculating each term:
\[ \frac{0.5}{8} = 0.0625 \]
\[ \frac{0.2}{2} = 0.1 \]

Adding these together:
\[ \frac{\Delta R}{R} = 0.0625 + 0.1 = 0.1625 \]

### Step 4: Convert to percentage
To find the percentage error:
\[ \text{Percentage error} = \frac{\Delta R}{R} \times 100 = 0.1625 \times 100 = 16.25\% \]

### Final Result
Thus, the value of resistance with its percentage error is:
\[ R = 4 \pm 16.25\% \, \Omega \]