Knowing how to calculate the power consumption of an appliance or device based on its resistance and current is crucial for understanding energy usage and managing electrical efficiency. The relationship between power (\(P\)), current (\(I\)), and resistance (\(R\)) is given by the formula:
\[ P = I^2 \cdot R \]
Where:
- \(P\) is the electric power (measured in watts, W)
- \(I\) is the electric current (measured in amperes, A)
- \(R\) is the resistance (measured in ohms, Ω)
Example 1: Electric Heater
Question: An electric heater has a resistance of 20 ohms and operates with a current of 10 amperes. How much power does the heater consume?
Calculation:
Given:
- \(R = 20\) Ω
- \(I = 10\) A
Using the formula:
\[ P = I^2 \cdot R = (10)^2 \cdot 20 = 100 \cdot 20 = 2000 \, \text{W} \]
Result: The electric heater consumes 2000 watts of power.
Example 2: Light Bulb
Question: A light bulb has a resistance of 240 ohms and operates with a current of 0.5 amperes. How much power does the light bulb consume?
Calculation:
Given:
- \(R = 240\) Ω
- \(I = 0.5\) A
Using the formula:
\[ P = I^2 \cdot R = (0.5)^2 \cdot 240 = 0.25 \cdot 240 = 60 \, \text{W} \]
Result: The light bulb consumes 60 watts of power.
Example 3: Electric Fan
Question: An electric fan has a resistance of 50 ohms and operates with a current of 2 amperes. How much power does the fan consume?
Calculation:
Given:
- \(R = 50\) Ω
- \(I = 2\) A
Using the formula:
\[ P = I^2 \cdot R = (2)^2 \cdot 50 = 4 \cdot 50 = 200 \, \text{W} \]
Result: The electric fan consumes 200 watts of power.
Calculating the power consumption of appliances and devices is essential for understanding their energy usage and ensuring efficient operation. By knowing the resistance and current, you can accurately determine how much power is being used, which helps in managing energy costs and ensuring that devices are operating within safe limits.
