How much energy is consumed when a current of 5 amperes flows through the filament (or element) of a heater having resistance of 100 ohms for two hours? Express it in joules.

Answer

To find the energy consumed by the heater, we can use the formula for electrical energy, which is given by:

\[ E = V \times I \times t \]

Where:
- \( E \) is the energy in joules (J)
- \( V \) is the voltage in volts (V)
- \( I \) is the current in amperes (A)
- \( t \) is the time in seconds (s)

However, we don't have the voltage directly, but we can find it using Ohm's Law, which states:

\[ V = I \times R \]

Where:
- \( R \) is the resistance in ohms (Ω)

### Step 1: Calculate the Voltage (V)
Given:
- Current \( I = 5 \, \text{A} \)
- Resistance \( R = 100 \, \text{Ω} \)

Using Ohm's Law:

\[ V = I \times R = 5 \, \text{A} \times 100 \, \text{Ω} = 500 \, \text{V} \]

### Step 2: Convert Time to Seconds
Given:
- Time \( t = 2 \, \text{hours} \)

Convert hours to seconds:

\[ t = 2 \, \text{hours} \times 3600 \, \text{seconds/hour} = 7200 \, \text{s} \]

### Step 3: Calculate the Energy (E)
Now we can substitute the values into the energy formula:

\[ E = V \times I \times t = 500 \, \text{V} \times 5 \, \text{A} \times 7200 \, \text{s} \]

Calculating:

\[ E = 500 \times 5 \times 7200 = 18000000 \, \text{J} \]

### Final Answer
The energy consumed is \( 18000000 \, \text{J} \) or \( 18 \, \text{MJ} \).

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