The heat produced in a long wire is characterised by resistance , current and time through which the current passes. If the errors in measuring these quantities are respectively 2%, 2% and 2% then total error in calculating the energy produced is

Options

A. `4%`
B. `6%`
C. `4//3%`
D. `8%`

Explanation

To solve the problem, we need to determine the total error in calculating the energy produced (heat) in a long wire, given the errors in measuring resistance (R), current (I), and time (T).

### Step-by-Step Solution:

1. **Identify the Formula for Heat Produced**:
The heat produced (H) in a wire is given by Joule's law:
\[ H = I^2 \cdot R \cdot T \]

2. **Determine the Relative Errors**:
We are given that the errors in measuring resistance (R), current (I), and time (T) are all 2%. This means:
- Error in current, \( \delta I/I = 2\% \)
- Error in resistance, \( \delta R/R = 2\% \)
- Error in time, \( \delta T/T = 2\% \)

3. **Calculate the Total Error in Heat Produced**:
To find the total error in heat produced, we can use the formula for the propagation of errors. Since the heat produced is proportional to the square of the current, the error in current will contribute double to the total error:
\[ \text{Total Error} = 2 \left(\frac{\delta I}{I}\right) + \left(\frac{\delta R}{R}\right) + \left(\frac{\delta T}{T}\right) \]

Substituting the values:
\[ \text{Total Error} = 2 \times 2\% + 2\% + 2\% \]
\[ \text{Total Error} = 4\% + 2\% + 2\% = 8\% \]

4. **Conclusion**:
The total error in calculating the energy produced (heat) is **8%**.

### Final Answer:
The total error in calculating the energy produced is **8%**.