Finding the electrical power when the voltage and resistance are known is a common task in electrical engineering. The relationship between these quantities is given by a specific formula, which can be calculated using algebraic manipulation.
The Formula: \( P = \dfrac{V^2}{R} \)
To find the power, we use the formula as it is:
\[ P = \dfrac{V^2}{R} \]
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: Power of a Ceiling Fan
Question: A ceiling fan operates at 220 volts and has a resistance of 110 ohms. What is the power consumption of the ceiling fan?
Calculation:
Given:
- \( V = 220 \) V
- \( R = 110 \) \(\Omega\)
Using the formula:
\[ P = \dfrac{V^2}{R} = \dfrac{220^2}{110} = \dfrac{48400}{110} = 440 \, \text{W} \]
Result: The power consumption of the ceiling fan is 440 watts.
Example 2: Power of a Toaster
Question: A toaster operates at 120 volts and has a resistance of 24 ohms. What is the power rating of the toaster?
Calculation:
Given:
- \( V = 120 \) V
- \( R = 24 \) \(\Omega\)
Using the formula:
\[ P = \dfrac{V^2}{R} = \dfrac{120^2}{24} = \dfrac{14400}{24} = 600 \, \text{W} \]
Result: The power rating of the toaster is 600 watts.
Example 3: Power of an LED Lamp
Question: An LED lamp operates at 12 volts and has a resistance of 6 ohms. What is the power consumption of the LED lamp?
Calculation:
Given:
- \( V = 12 \) V
- \( R = 6 \) \(\Omega\)
Using the formula:
\[ P = \dfrac{V^2}{R} = \dfrac{12^2}{6} = \dfrac{144}{6} = 24 \, \text{W} \]
Result: The power consumption of the LED lamp is 24 watts.
