Electric power is a fundamental concept in understanding how electrical devices operate. Knowing how to calculate power from voltage and resistance can help in designing circuits, selecting components, and optimizing energy consumption. This article will guide you through calculating electric power (\( P \)) when voltage (\( V \)) and resistance (\( R \)) are given, using the formula \( P = \dfrac{V^2}{R} \). We’ll illustrate with three practical examples.
Formula to Determine Electric Power
Electric power (\( P \)) can be calculated using the formula:
\[ P = \dfrac{V^2}{R} \]
where:
- \( P \) is the power (in watts, W),
- \( V \) is the voltage (in volts, V),
- \( R \) is the resistance (in ohms, \(\Omega\)).
Example 1: Power Consumption of a Light Bulb
Scenario: You have a light bulb rated at \( 240 \, \text{V} \) and a resistance of \( 960 \, \Omega \). How much power does it consume?
Step-by-Step Calculation:
1. Given:
\[ V = 240 \, \text{V} \]
\[ R = 960 \, \Omega \]
2. Substitute Values into the Power Formula:
\[ P = \dfrac{V^2}{R} \]
\[ P = \dfrac{240^2}{960} \]
3. Perform the Calculation:
\[ P = \dfrac{57600}{960} \]
\[ P = 60 \, \text{W} \]
Final Value
The power consumed by the light bulb is:
\[ P = 60 \, \text{W} \]
Example 2: Power Output of a Heater
Scenario: A heater operates at \( 220 \, \text{V} \) and has a resistance of \( 44 \, \Omega \). What is its power output?
Step-by-Step Calculation:
1. Given:
\[ V = 220 \, \text{V} \]
\[ R = 44 \, \Omega \]
2. Substitute Values into the Power Formula:
\[ P = \dfrac{V^2}{R} \]
\[ P = \dfrac{220^2}{44} \]
3. Perform the Calculation:
\[ P = \dfrac{48400}{44} \]
\[ P = 1100 \, \text{W} \]
Final Value
The power output of the heater is:
\[ P = 1100 \, \text{W} \]
Example 3: Power Rating of a Resistor
Scenario: A resistor in a circuit has a voltage of \( 12 \, \text{V} \) across it and a resistance of \( 48 \, \Omega \). What is the power rating of the resistor?
Step-by-Step Calculation:
1. Given:
\[ V = 12 \, \text{V} \]
\[ R = 48 \, \Omega \]
2. Substitute Values into the Power Formula:
\[ P = \dfrac{V^2}{R} \]
\[ P = \dfrac{12^2}{48} \]
3. Perform the Calculation:
\[ P = \dfrac{144}{48} \]
\[ P = 3 \, \text{W} \]
Final Value
The power rating of the resistor is:
\[ P = 3 \, \text{W} \]
Summary
In the examples provided:
1. A light bulb with \( 240 \, \text{V} \) and \( 960 \, \Omega \) resistance consumes \( 60 \, \text{W} \).
2. A heater with \( 220 \, \text{V} \) and \( 44 \, \Omega \) resistance outputs \( 1100 \, \text{W} \).
3. A resistor with \( 12 \, \text{V} \) and \( 48 \, \Omega \) resistance has a power rating of \( 3 \, \text{W} \).
