Calculating the resistance when the power and current are known is fundamental for various electrical applications. This relationship is expressed through a specific formula, which we will explore with practical examples.
The Formula: \( P = I^2 \cdot R \)
To find the resistance, we rearrange the formula as follows:
\[ R = \dfrac{P}{I^2} \]
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: Resistance of a Hair Dryer
Question: A hair dryer operates at 1800 watts with a current of 7.5 amperes. What is the resistance?
Calculation:
Given:
- \( P = 1800 \) W
- \( I = 7.5 \) A
Using the formula:
\[ R = \dfrac{P}{I^2} = \dfrac{1800}{(7.5)^2} = \dfrac{1800}{56.25} = 32 \, \Omega \]
Result: The resistance of the hair dryer is 32 ohms.
Example 2: Resistance of an Air Conditioner
Question: An air conditioner consumes 2400 watts of power and operates with a current of 10 amperes. What is the resistance?
Calculation:
Given:
- \( P = 2400 \) W
- \( I = 10 \) A
Using the formula:
\[ R = \dfrac{P}{I^2} = \dfrac{2400}{(10)^2} = \dfrac{2400}{100} = 24 \, \Omega \]
Result: The resistance of the air conditioner is 24 ohms.
Example 3: Resistance of a Microwave Oven
Question: A microwave oven operates at 1200 watts with a current of 5 amperes. What is the resistance?
Calculation:
Given:
- \( P = 1200 \) W
- \( I = 5 \) A
Using the formula:
\[ R = \dfrac{P}{I^2} = \dfrac{1200}{(5)^2} = \dfrac{1200}{25} = 48 \, \Omega \]
Result: The resistance of the microwave oven is 48 ohms.
