How To Find Resistance Using Power And Voltage

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 $R={\displaystyle \frac{V^2}{P}}$. We’ll illustrate with three practical examples.

Formula to Determine Resistance

Resistance ($R$) can be calculated using the formula:

$$R={\displaystyle \frac{V^2}{P}}$$

where:

• $R$ is the resistance (in ohms, $\mathrm{\Omega }$),
• $V$ 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:

  $$R={\displaystyle \frac{V^2}{P}}$$

  $$R={\displaystyle \frac{{230}^2}{2000}}$$

3. Perform the Calculation:

  $$R={\displaystyle \frac{52900}{2000}}$$

  $$R=26.45\mathrm{\Omega }$$

Final Value

The resistance of the electric heater is:

$$R=26.45\mathrm{\Omega }$$

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:

  $$R={\displaystyle \frac{V^2}{P}}$$

  $$R={\displaystyle \frac{{19}^2}{65}}$$

3. Perform the Calculation:

  $$R={\displaystyle \frac{361}{65}}$$

  $$R\approx 5.55\mathrm{\Omega }$$

Final Value

The resistance in the laptop charger is approximately:

$$R\approx 5.55\mathrm{\Omega }$$

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:

  $$R={\displaystyle \frac{V^2}{P}}$$

  $$R={\displaystyle \frac{{110}^2}{1500}}$$

3. Perform the Calculation:

  $$R={\displaystyle \frac{12100}{1500}}$$

  $$R\approx 8.07\mathrm{\Omega }$$

Final Value

The resistance of the hair dryer is approximately:

$$R\approx 8.07\mathrm{\Omega }$$

Summary

To find the resistance ($R$) given the power ($P$) and voltage ($V$), use the formula:

$$R={\displaystyle \frac{V^2}{P}}$$

In the examples provided:

1. An electric heater operating at $230\text{V}$ and consuming $2000\text{W}$ has a resistance of $26.45\mathrm{\Omega }$.

2. A laptop charger using $19\text{V}$ and outputting $65\text{W}$ has a resistance of approximately $5.55\mathrm{\Omega }$.

3. A hair dryer running at $110\text{V}$ and consuming $1500\text{W}$ has a resistance of approximately $8.07\mathrm{\Omega }$.