An electric heater of resistance 6 ohm is run for 10 minutes on a 120 volt line. The energy liberated in this period of time is

Options

A. `7.2xx10^(3)J`
B. `14.4xx10^(5) J`
C. `43.2xx10^(-4)J`
D. `28.8xx10^(4)J`

Answer

To solve the problem of finding the energy liberated by an electric heater with a resistance of 6 ohms running on a 120-volt line for 10 minutes, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Time from Minutes to Seconds**:
- The heater runs for 10 minutes. We need to convert this time into seconds.
\[ \text{Time (t)} = 10 \text{ minutes} \times 60 \text{ seconds/minute} = 600 \text{ seconds} \]

2. **Use the Power Formula**:
- The power (P) consumed by the heater can be calculated using the formula:
\[ P = \frac{V^2}{R} \]
where \( V \) is the voltage and \( R \) is the resistance.

3. **Substitute the Given Values**:
- Here, \( V = 120 \text{ volts} \) and \( R = 6 \text{ ohms} \).
\[ P = \frac{(120)^2}{6} \]

4. **Calculate Power**:
- Calculate \( (120)^2 \):
\[ (120)^2 = 14400 \]
- Now substitute this value into the power formula:
\[ P = \frac{14400}{6} = 2400 \text{ watts} \]

5. **Calculate Energy**:
- The energy (E) liberated can be calculated using the formula:
\[ E = P \times t \]
- Substitute the power and time:
\[ E = 2400 \text{ watts} \times 600 \text{ seconds} \]

6. **Final Calculation**:
\[ E = 2400 \times 600 = 1440000 \text{ joules} \]
- This can also be expressed in scientific notation:
\[ E = 1.44 \times 10^6 \text{ joules} \]

### Final Answer:
The energy liberated in this period of time is \( 1.44 \times 10^6 \) joules.

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