The voltage and current in a conductor are measured as `(50pm2)V and (5pm0.2)A` The percentage error in the calculation of resistance is

Options

A. `4%`
B. `5%`
C. `7%`
D. `8%`

Answer

To calculate the percentage error in the resistance based on the given voltage and current measurements, we can follow these steps:

### Step 1: Understand Ohm's Law
According to Ohm's Law, the resistance \( R \) can be calculated using the formula:
\[ R = \frac{V}{I} \]
where \( V \) is the voltage and \( I \) is the current.

### Step 2: Identify Given Values
From the problem, we have:
- Voltage \( V = 50 \pm 2 \) V
- Current \( I = 5 \pm 0.2 \) A

### Step 3: Calculate the Absolute Errors
The absolute errors in voltage and current are:
- \( \Delta V = 2 \) V
- \( \Delta I = 0.2 \) A

### Step 4: Calculate the Percentage Errors
The percentage errors in voltage and current can be calculated using the formulas:
\[ \text{Percentage Error in } V = \frac{\Delta V}{V} \times 100 = \frac{2}{50} \times 100 \]
\[ \text{Percentage Error in } I = \frac{\Delta I}{I} \times 100 = \frac{0.2}{5} \times 100 \]

Calculating these:
- Percentage Error in \( V \):
\[ \frac{2}{50} \times 100 = 4\% \]
- Percentage Error in \( I \):
\[ \frac{0.2}{5} \times 100 = 4\% \]

### Step 5: Calculate the Total Percentage Error in Resistance
The total percentage error in resistance can be calculated using the formula:
\[ \text{Percentage Error in } R = \text{Percentage Error in } V + \text{Percentage Error in } I \]
Substituting the values:
\[ \text{Percentage Error in } R = 4\% + 4\% = 8\% \]

### Final Answer
The percentage error in the calculation of resistance is:
\[ \boxed{8\%} \]