Understanding resistance in electrical circuits is key for managing how components react to applied voltage and power. This article will show you how to find resistance (\( R \)) when power (\( P \)) and voltage (\( V \)) are given, using the formula \( R = \dfrac{V^2}{P} \). We’ll illustrate with three practical examples.
Formula to Determine Resistance
Resistance (\( R \)) can be calculated using the formula:
\[ R = \dfrac{V^2}{P} \]
where:
- \( R \) is the resistance (in ohms, \(\Omega\)),
- \( V \) is the voltage (in volts, V),
- \( P \) is the power (in watts, W).
Example 1: Resistance of an Electric Heater
Scenario: An electric heater operates at \( 230 \, \text{V} \) and consumes \( 2000 \, \text{W} \) of power. What is the resistance of the heater?
Step-by-Step Calculation:
1. Given:
\[ V = 230 \, \text{V} \]
\[ P = 2000 \, \text{W} \]
2. Substitute Values into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{230^2}{2000} \]
3. Perform the Calculation:
\[ R = \dfrac{52900}{2000} \]
\[ R = 26.45 \, \Omega \]
Final Value
The resistance of the electric heater is:
\[ R = 26.45 \, \Omega \]
Example 2: Resistance in a Laptop Charger
Scenario: A laptop charger uses \( 19 \, \text{V} \) and outputs \( 65 \, \text{W} \). What is the resistance?
Step-by-Step Calculation:
1. Given:
\[ V = 19 \, \text{V} \]
\[ P = 65 \, \text{W} \]
2. Substitute Values into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{19^2}{65} \]
3. Perform the Calculation:
\[ R = \dfrac{361}{65} \]
\[ R \approx 5.55 \, \Omega \]
Final Value
The resistance in the laptop charger is approximately:
\[ R \approx 5.55 \, \Omega \]
Example 3: Resistance of a Hair Dryer
Scenario: A hair dryer runs at \( 110 \, \text{V} \) and consumes \( 1500 \, \text{W} \). Find the resistance.
Step-by-Step Calculation:
1. Given:
\[ V = 110 \, \text{V} \]
\[ P = 1500 \, \text{W} \]
2. Substitute Values into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{110^2}{1500} \]
3. Perform the Calculation:
\[ R = \dfrac{12100}{1500} \]
\[ R \approx 8.07 \, \Omega \]
Final Value
The resistance of the hair dryer is approximately:
\[ R \approx 8.07 \, \Omega \]
Summary
To find the resistance (\( R \)) given the power (\( P \)) and voltage (\( V \)), use the formula:
\[ R = \dfrac{V^2}{P} \]
In the examples provided:
1. An electric heater operating at \( 230 \, \text{V} \) and consuming \( 2000 \, \text{W} \) has a resistance of \( 26.45 \, \Omega \).
2. A laptop charger using \( 19 \, \text{V} \) and outputting \( 65 \, \text{W} \) has a resistance of approximately \( 5.55 \, \Omega \).
3. A hair dryer running at \( 110 \, \text{V} \) and consuming \( 1500 \, \text{W} \) has a resistance of approximately \( 8.07 \, \Omega \).
