The heat produced (in calories) in a resistance R when a current I amperes flows through it for t seconds is given by the expression

Options

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

Answer

To solve the problem of calculating the heat produced in a resistance when a current flows through it, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Heat Produced**:
The heat produced (H) in a resistor when a current (I) flows through it for a time (t) is given by the formula:
\[ H = I^2 R t \]
where:
- \(H\) is the heat produced 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 produced in calories, we need to convert joules to calories. We know that:
\[ 1 \text{ calorie} = 4.2 \text{ joules} \]
Therefore, to convert joules to calories, we can use the conversion factor:
\[ H \text{ (in calories)} = \frac{H \text{ (in joules)}}{4.2} \]

3. **Substitute the Heat Formula into the Conversion**:
Substitute the expression for heat produced in joules into the conversion formula:
\[ H \text{ (in calories)} = \frac{I^2 R t}{4.2} \]

4. **Final Expression**:
Thus, the final expression for the heat produced in calories when a current I flows through a resistance R for time t is:
\[ H = \frac{I^2 R t}{4.2} \]

5. **Select the Correct Option**:
Based on the derived expression, we can conclude that the correct answer is:
\[ \text{Option A: } \frac{I^2 R t}{4.2} \]