Calculating electric energy when the power and time are known is essential in understanding the energy consumption of electrical devices. This relationship is expressed through a specific formula, which we will explore with practical examples.
The Formula: \( P = \dfrac{E}{t} \)
To find the electric energy, we rearrange the formula as follows:
\[ E = P \cdot t \]
Where:
- \( P \) is the electric power (measured in watts, W)
- \( E \) is the electric energy (measured in joules, J)
- \( t \) is the time (measured in seconds, s)
Example 1: Energy Consumption of a Heater
Question: A heater operates at a power rating of 1500 watts for 1800 seconds. How much energy does it consume?
Calculation:
Given:
- \( P = 1500 \) W
- \( t = 1800 \) s
Using the formula:
\[ E = P \cdot t = 1500 \cdot 1800 = 2,700,000 \, \text{J} \]
Result: The heater consumes 2,700,000 joules of energy.
Example 2: Energy Usage of a Washing Machine
Question: A washing machine runs at 800 watts for 3600 seconds. How much energy does it use?
Calculation:
Given:
- \( P = 800 \) W
- \( t = 3600 \) s
Using the formula:
\[ E = P \cdot t = 800 \cdot 3600 = 2,880,000 \, \text{J} \]
Result: The washing machine uses 2,880,000 joules of energy.
Example 3: Energy Requirement of a Computer
Question: A computer operates at a power rating of 200 watts for 7200 seconds. How much energy is required?
Calculation:
Given:
- \( P = 200 \) W
- \( t = 7200 \) s
Using the formula:
\[ E = P \cdot t = 200 \cdot 7200 = 1,440,000 \, \text{J} \]
Result: The computer requires 1,440,000 joules of energy.
