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. (a)`8%`
B. (b)`4%`
C. (c)`20%`
D. (d)`10%`

Answer

To solve the problem of calculating 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) = 100 ± 4 V
- Current (I) = 5 ± 0.2 A

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

### Step 3: Determine the relative errors in voltage and current
The percentage error in a quantity can be expressed as:
\[ \text{Percentage Error} = \left( \frac{\Delta x}{x} \right) \times 100 \]
where \( \Delta x \) is the uncertainty in the measurement and \( x \) is the measured value.

#### For Voltage:
- Change in Voltage (\( \Delta V \)) = 4 V
- Measured Voltage (V) = 100 V

The percentage error in voltage is:
\[ \text{Percentage Error in V} = \left( \frac{4}{100} \right) \times 100 = 4\% \]

#### For Current:
- Change in Current (\( \Delta I \)) = 0.2 A
- Measured Current (I) = 5 A

The percentage error in current is:
\[ \text{Percentage Error in I} = \left( \frac{0.2}{5} \right) \times 100 = 4\% \]

### Step 4: Calculate the total percentage error in resistance
When calculating resistance, the percentage errors in voltage and current add up. Therefore, the total percentage error in resistance is given by:
\[ \text{Percentage Error in R} = \text{Percentage Error in V} + \text{Percentage Error in I} \]

Substituting the values:
\[ \text{Percentage Error in R} = 4\% + 4\% = 8\% \]

### Step 5: Conclusion
The percentage error in the calculation of resistance is:
\[ \boxed{8\%} \]

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