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: Identify the given values
- Voltage (V) = 50 V with an uncertainty (ΔV) = 2 V
- Current (I) = 5 A with an uncertainty (ΔI) = 0.2 A

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

### Step 3: Calculate the relative error in resistance
The relative error in resistance can be calculated using the formula:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} + \frac{\Delta I}{I} \]

### Step 4: Substitute the values into the formula
- Calculate the relative error due to voltage:
\[ \frac{\Delta V}{V} = \frac{2}{50} = 0.04 \]

- Calculate the relative error due to current:
\[ \frac{\Delta I}{I} = \frac{0.2}{5} = 0.04 \]

### Step 5: Add the relative errors
Now, add the two relative errors:
\[ \frac{\Delta R}{R} = 0.04 + 0.04 = 0.08 \]

### Step 6: Convert relative error to percentage error
To find the percentage error, multiply the relative error by 100:
\[ \text{Percentage Error} = 0.08 \times 100 = 8\% \]

### Final Answer
The percentage error in the calculation of resistance is **8%**.

---