The percentage error in the measurement of the voltage V is 3% and in the measurement of the current is 2%. The percentage error in the measurement of the resistance is

Options

A. 0.03
B. 0.02
C. 0.01
D. 0.05

Answer

To find the percentage error in the measurement of resistance (R), we can use Ohm's law, which states that:

\[ V = I \cdot R \]

From this, we can express resistance as:

\[ R = \frac{V}{I} \]

### Step 1: Understand the relationship between errors
According to the rules of error propagation, when we have a quotient (like R = V/I), the percentage errors add up. Therefore, the percentage error in resistance can be calculated using the formula:

\[ \text{Percentage error in } R = \text{Percentage error in } V + \text{Percentage error in } I \]

### Step 2: Identify the given percentage errors
From the problem, we know:
- Percentage error in voltage (V) = 3%
- Percentage error in current (I) = 2%

### Step 3: Substitute the values into the formula
Now we can substitute the known values into the formula:

\[ \text{Percentage error in } R = 3\% + 2\% \]

### Step 4: Calculate the total percentage error
Adding these values together gives:

\[ \text{Percentage error in } R = 5\% \]

### Conclusion
Thus, the percentage error in the measurement of resistance is **5%**.

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