An electric heater of resistance `15Omega` is run for 8 sec on 120 V line. The energy liberated in this period of time is

Options

A. `7.68xx10^3J`
B. `14.4xx10^5J`
C. `4.32xx10^4J`
D. `28.8xx10^4J`

Answer

To solve the problem of calculating the energy liberated by an electric heater with a resistance of 15 ohms running on a 120 V line for 8 seconds, we can follow these steps:

### Step 1: Calculate the Current
Using Ohm's Law, we can find the current (I) flowing through the heater. Ohm's Law states that:

\[ V = I \times R \]

Where:
- \( V \) is the voltage (120 V)
- \( I \) is the current (in amperes)
- \( R \) is the resistance (15 ohms)

Rearranging the formula to solve for current gives us:

\[ I = \frac{V}{R} \]

Substituting the known values:

\[ I = \frac{120 \, \text{V}}{15 \, \Omega} = 8 \, \text{A} \]

### Step 2: Calculate the Energy
The energy (E) liberated can be calculated using the formula:

\[ E = I^2 \times R \times T \]

Where:
- \( E \) is the energy (in joules)
- \( I \) is the current (8 A)
- \( R \) is the resistance (15 ohms)
- \( T \) is the time (8 seconds)

Substituting the values into the formula:

\[ E = (8 \, \text{A})^2 \times 15 \, \Omega \times 8 \, \text{s} \]

Calculating \( I^2 \):

\[ I^2 = 8^2 = 64 \]

Now substituting back into the energy equation:

\[ E = 64 \times 15 \times 8 \]

### Step 3: Perform the Multiplication
First, calculate \( 64 \times 15 \):

\[ 64 \times 15 = 960 \]

Now multiply by 8:

\[ E = 960 \times 8 = 7680 \, \text{J} \]

### Step 4: Convert to Scientific Notation
To express the energy in scientific notation, we can write:

\[ E = 7680 \, \text{J} = 7.68 \times 10^3 \, \text{J} \]

### Final Answer
The energy liberated in this period of time is:

\[ \boxed{7.68 \times 10^3 \, \text{J}} \]

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