In the experiment of verification of Ohm's law the error in the current measurement is 1%, while that in the voltage measurement is 2%. The error in the resistance has a maximum value of

Options

A. 1%
B. 2%
C. 3%
D. none of these

Answer

To find the maximum error in resistance based on the given errors in current and voltage measurements, we can follow these steps:

### Step 1: Understand the relationship from Ohm's Law
Ohm's Law states that:
\[ V = I \times R \]
Where:
- \( V \) is the voltage,
- \( I \) is the current,
- \( R \) is the resistance.

### Step 2: Identify the given errors
From the problem, we know:
- The error in current measurement (\( \Delta I/I \)) is 1%.
- The error in voltage measurement (\( \Delta V/V \)) is 2%.

### Step 3: Write the formula for error in resistance
Using the relationship from Ohm's Law, we can express the error in resistance (\( \Delta R/R \)):
\[ \frac{\Delta V}{V} = \frac{\Delta I}{I} + \frac{\Delta R}{R} \]
Rearranging this gives us:
\[ \frac{\Delta R}{R} = \frac{\Delta V}{V} - \frac{\Delta I}{I} \]

### Step 4: Substitute the values of errors
Substituting the given values into the equation:
- \( \frac{\Delta V}{V} = 2\% \)
- \( \frac{\Delta I}{I} = 1\% \)

So we have:
\[ \frac{\Delta R}{R} = 2\% + 1\% \]

### Step 5: Calculate the maximum error in resistance
Now, adding the errors:
\[ \frac{\Delta R}{R} = 2\% + 1\% = 3\% \]

### Conclusion
The maximum error in resistance is:
\[ \Delta R = 3\% \]

### Final Answer
Thus, the maximum error in the resistance is **3%**.

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