The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively, then maximum error in measuring the heat is

Options

A. 0.08
B. 0.06
C. 0.18
D. 0.12

Explanation

To solve the problem of finding the maximum error in measuring the heat generated in a circuit, we can follow these steps:

### Step 1: Understand the formula for heat generated
The heat generated (H) in a circuit can be expressed using the formula:
\[ H = I^2 \cdot R \cdot T \]
where:
- \( I \) = current
- \( R \) = resistance
- \( T \) = time

### Step 2: Identify the errors in measurements
We are given the percentage errors in measuring resistance, current, and time:
- Error in resistance (\( \delta R/R \)) = 1% = 0.01
- Error in current (\( \delta I/I \)) = 2% = 0.02
- Error in time (\( \delta T/T \)) = 1% = 0.01

### Step 3: Use the formula for maximum error
The maximum error in measuring heat can be calculated using the formula for propagation of errors in multiplication:
\[ \frac{\delta H}{H} = 2 \cdot \frac{\delta I}{I} + \frac{\delta R}{R} + \frac{\delta T}{T} \]
Here, the factor of 2 in front of \( \frac{\delta I}{I} \) arises because the current \( I \) is squared in the heat formula.

### Step 4: Substitute the values into the error formula
Substituting the values of the errors into the formula:
\[ \frac{\delta H}{H} = 2 \cdot 0.02 + 0.01 + 0.01 \]

### Step 5: Calculate the total maximum error
Now, calculate the total:
\[ \frac{\delta H}{H} = 0.04 + 0.01 + 0.01 = 0.06 \]

### Step 6: Interpret the result
The maximum error in measuring the heat generated is:
\[ \delta H = 0.06 \]
This can also be expressed as a percentage:
\[ \delta H = 6\% \]

### Conclusion
The maximum error in measuring the heat generated in the circuit is **6%**.

---