Calculating the electric power using current and resistance is essential for understanding the energy consumption of electrical devices. The relationship between these quantities is expressed through a specific formula, which we will explore with practical examples.
The Formula: \( P = I^2 \cdot R \)
Where:
- \( P \) is the electric power (measured in watts, W)
- \( I \) is the current (measured in amperes, A)
- \( R \) is the resistance (measured in ohms, \(\Omega\))
Example 1: Power Consumption of a Light Bulb
Question: A light bulb operates with a current of 0.5 amperes and has a resistance of 240 ohms. What is the power consumption of the light bulb?
Calculation:
Given:
- \( I = 0.5 \) A
- \( R = 240 \) \(\Omega\)
Using the formula:
\[ P = I^2 \cdot R = (0.5)^2 \cdot 240 = 0.25 \cdot 240 = 60 \, \text{W} \]
Result: The power consumption of the light bulb is 60 watts.
Example 2: Power Output of an Electric Heater
Question: An electric heater operates with a current of 10 amperes and has a resistance of 20 ohms. What is the power output of the electric heater?
Calculation:
Given:
- \( I = 10 \) A
- \( R = 20 \) \(\Omega\)
Using the formula:
\[ P = I^2 \cdot R = (10)^2 \cdot 20 = 100 \cdot 20 = 2000 \, \text{W} \]
Result: The power output of the electric heater is 2000 watts.
Example 3: Power Consumption of a Fan
Question: A fan operates with a current of 2 amperes and has a resistance of 30 ohms. What is the power consumption of the fan?
Calculation:
Given:
- \( I = 2 \) A
- \( R = 30 \) \(\Omega\)
Using the formula:
\[ P = I^2 \cdot R = (2)^2 \cdot 30 = 4 \cdot 30 = 120 \, \text{W} \]
Result: The power consumption of the fan is 120 watts.
