Heat developed in an electric wire of resistance Rohm by current / ampere for a time t second is

Options

A. `((I ^(2) Rt)/(4.2))`cal
B. `((I ^(2) t )/( 4.2 R))`cal
C. `((I ^(2) R)/(4.2 t)) ` cal
D. `((Rt)/(4.2 I ^(2)))` cal

Answer

To solve the problem of calculating the heat developed in an electric wire of resistance \( R \) ohms by a current \( I \) amperes for a time \( t \) seconds, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Heat**:
The heat developed in a conductor due to electric current can be calculated using the formula:
\[ H = I^2 R t \]
where:
- \( H \) is the heat developed (in Joules),
- \( I \) is the current (in Amperes),
- \( R \) is the resistance (in Ohms),
- \( t \) is the time (in seconds).

2. **Convert Joules to Calories**:
Since the question asks for the heat in calories, we need to convert the heat from Joules to Calories. The conversion factor is:
\[ 1 \text{ Calorie} = 4.2 \text{ Joules} \]
Therefore, to convert Joules to Calories, we use:
\[ \text{Calories} = \frac{\text{Joules}}{4.2} \]

3. **Substituting the Heat Formula**:
Substitute the heat formula into the conversion:
\[ H \text{ (in Calories)} = \frac{H \text{ (in Joules)}}{4.2} = \frac{I^2 R t}{4.2} \]

4. **Final Expression**:
The final expression for the heat developed in calories is:
\[ H = \frac{I^2 R t}{4.2} \text{ Calories} \]

### Conclusion:
Thus, the heat developed in an electric wire of resistance \( R \) ohms by a current \( I \) amperes for a time \( t \) seconds is:
\[ H = \frac{I^2 R t}{4.2} \text{ Calories} \]