Understanding how to find electric current (\(I\)) when you know the power (\(P\)) and resistance (\(R\)) is essential for various electrical applications. The relationship between power, current, and resistance is given by the formula:
\[ P = I^2 \cdot R \]
To find the electric current, rearrange the formula to solve for \(I\):
\[ I = \sqrt{\dfrac{P}{R}} \]
Where:
- \(P\) is the electric power (measured in watts, W)
- \(R\) is the resistance (measured in ohms, Ω)
- \(I\) is the electric current (measured in amperes, A)
Example 1: Electric Kettle
Question: An electric kettle uses 2000 watts of power and has a resistance of 24 ohms. What is the electric current flowing through the kettle?
Calculation:
Given:
- \(P = 2000\) W
- \(R = 24\) Ω
Using the formula:
\[ I = \sqrt{\dfrac{P}{R}} = \sqrt{\dfrac{2000}{24}} \approx 9.13 \, \text{A} \]
Result: The electric current flowing through the electric kettle is approximately 9.13 amperes.
Example 2: Electric Toaster
Question: An electric toaster operates at 1000 watts of power and has a resistance of 48 ohms. What is the electric current in the toaster?
Calculation:
Given:
- \(P = 1000\) W
- \(R = 48\) Ω
Using the formula:
\[ I = \sqrt{\dfrac{P}{R}} = \sqrt{\dfrac{1000}{48}} \approx 4.58 \, \text{A} \]
Result: The electric current in the toaster is approximately 4.58 amperes.
Example 3: Hair Dryer
Question: A hair dryer uses 1500 watts of power and has a resistance of 30 ohms. What is the electric current flowing through the hair dryer?
Calculation:
Given:
- \(P = 1500\) W
- \(R = 30\) Ω
Using the formula:
\[ I = \sqrt{\dfrac{P}{R}} = \sqrt{\dfrac{1500}{30}} \approx 7.07 \, \text{A} \]
Result: The electric current flowing through the hair dryer is approximately 7.07 amperes.
Understanding how to calculate electric current using power and resistance is crucial for designing and troubleshooting electrical appliances. These calculations ensure that devices operate safely and efficiently, preventing overloading and potential hazards.
