When the voltage and current in a conductor are measured as `(100pm4 ) V and (5pm0.2 )` A, then the percentage of error in the calculation of resistance is

Options

A. `8%`
B. `4%`
C. `20%`
D. `10%`

Answer

To find the percentage of error in the calculation of resistance when given the voltage and current with their respective uncertainties, we can follow these steps:

### Step 1: Identify the given values
- Voltage (V) = \(100 \pm 4 \, V\)
- Current (I) = \(5 \pm 0.2 \, A\)

### Step 2: Write the formula for resistance
The formula for resistance (R) is given by:
\[ R = \frac{V}{I} \]

### Step 3: Calculate the relative error in voltage and current
The relative error in voltage (\(\Delta V\)) and current (\(\Delta I\)) can be calculated as follows:
- Relative error in voltage:
\[ \frac{\Delta V}{V} = \frac{4}{100} = 0.04 \]
- Relative error in current:
\[ \frac{\Delta I}{I} = \frac{0.2}{5} = 0.04 \]

### Step 4: Calculate the total relative error in resistance
The total relative error in resistance can be calculated using the formula:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \left(-\frac{\Delta I}{I}\right) \]
However, since we are looking for the maximum error, we will add the relative errors:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]
Substituting the values:
\[ \frac{\Delta R}{R} = 0.04 + 0.04 = 0.08 \]

### Step 5: Convert the relative error to percentage
To convert the relative error to a percentage, multiply by 100:
\[ \text{Percentage error} = 0.08 \times 100 = 8\% \]

### Final Answer
The percentage of error in the calculation of resistance is \(8\%\).

---