Determining the resistance when the power and voltage are known is essential in various electrical scenarios. The relationship between these quantities can be calculated using a specific formula and algebraic rearrangement.
The Formula: \( P = \dfrac{V^2}{R} \)
To find the resistance, we rearrange the formula as follows:
\[ R = \dfrac{V^2}{P} \]
Where:
- \( P \) is the power (measured in watts, W)
- \( V \) is the voltage (measured in volts, V)
- \( R \) is the resistance (measured in ohms, \(\Omega\))
Example 1: Resistance of a Hair Dryer
Question: A hair dryer operates at 1800 watts and 120 volts. What is the resistance of the hair dryer?
Calculation:
Given:
- \( P = 1800 \) W
- \( V = 120 \) V
Using the formula:
\[ R = \dfrac{V^2}{P} = \dfrac{120^2}{1800} = \dfrac{14400}{1800} = 8 \, \Omega \]
Result: The resistance of the hair dryer is 8 ohms.
Example 2: Resistance of an Electric Iron
Question: An electric iron uses 1100 watts of power and operates on 220 volts. What is the resistance of the iron?
Calculation:
Given:
- \( P = 1100 \) W
- \( V = 220 \) V
Using the formula:
\[ R = \dfrac{V^2}{P} = \dfrac{220^2}{1100} = \dfrac{48400}{1100} \approx 44 \, \Omega \]
Result: The resistance of the electric iron is approximately 44 ohms.
Example 3: Resistance of a Washing Machine
Question: A washing machine operates with a power of 2400 watts and a voltage of 240 volts. What is the resistance?
Calculation:
Given:
- \( P = 2400 \) W
- \( V = 240 \) V
Using the formula:
\[ R = \dfrac{V^2}{P} = \dfrac{240^2}{2400} = \dfrac{57600}{2400} = 24 \, \Omega \]
Result: The resistance of the washing machine is 24 ohms.
