An electric heater of resistance `8 Omega` draws `15 A` from the service mains for `2` hours. Calculate the rate at which heat is developed in the heater.

Options

A. `1500 J/s`
B. `2000 J/s`
C. `1000 J/s`
D. `1800 J/s`

Explanation

To calculate the rate at which heat is developed in the electric heater, we can use the formula for power in an electrical circuit. The power (P) developed in a resistor can be calculated using the formula:

\[ P = I^2 \times R \]

Where:
- \( P \) is the power in watts (W),
- \( I \) is the current in amperes (A),
- \( R \) is the resistance in ohms (Ω).

### Step-by-step Solution:

1. **Identify the given values:**
- Resistance \( R = 8 \, \Omega \)
- Current \( I = 15 \, A \)

2. **Substitute the values into the power formula:**
\[ P = I^2 \times R \]
\[ P = (15 \, A)^2 \times 8 \, \Omega \]

3. **Calculate \( I^2 \):**
\[ I^2 = 15^2 = 225 \]

4. **Multiply by the resistance:**
\[ P = 225 \times 8 \]

5. **Calculate the power:**
\[ P = 1800 \, W \]

6. **Convert watts to joules per second (if necessary):**
Since \( 1 \, W = 1 \, \text{joule/second} \), we can say:
\[ P = 1800 \, \text{joules/second} \]

### Final Answer:
The rate at which heat is developed in the heater is \( 1800 \, W \) or \( 1800 \, \text{joules/second} \).

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