If voltage `V=(100pm5)` V and current `I=(10pm0.2)` A, the percentage error in resistance `R` is

Options

A. `5.2`%
B. 0.25
C. 0.07
D. 0.1

Explanation

To find the percentage error in resistance \( R \) when given the voltage \( V \) and current \( I \) with their respective errors, we can follow these steps:

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

### Step 2: Identify the values and their uncertainties
From the problem, we have:
- Voltage \( V = 100 \pm 5 \) V
- Current \( I = 10 \pm 0.2 \) A

### Step 3: Calculate the nominal value of resistance
Using the values of \( V \) and \( I \):
\[ R = \frac{100 \, \text{V}}{10 \, \text{A}} = 10 \, \Omega \]

### Step 4: Calculate the relative errors in voltage and current
The relative error in voltage \( \delta V \) is given by:
\[ \frac{\delta V}{V} = \frac{5}{100} = 0.05 \]

The relative error in current \( \delta I \) is given by:
\[ \frac{\delta I}{I} = \frac{0.2}{10} = 0.02 \]

### Step 5: Calculate the total relative error in resistance
The total relative error in resistance \( R \) can be calculated using the formula:
\[ \frac{\delta R}{R} = \frac{\delta V}{V} + \frac{\delta I}{I} \]
Substituting the values:
\[ \frac{\delta R}{R} = 0.05 + 0.02 = 0.07 \]

### Step 6: Calculate the percentage error in resistance
To find the percentage error, we multiply the relative error by 100:
\[ \text{Percentage error in } R = \frac{\delta R}{R} \times 100 = 0.07 \times 100 = 7\% \]

### Final Answer
The percentage error in resistance \( R \) is \( 7\% \).

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