Voltage is crucial in electrical systems for determining the potential difference across components. This article explains how to find voltage (\( V \)) when power (\( P \)) and resistance (\( R \)) are known, using the formula \( V = \sqrt{P \cdot R} \). We’ll use three practical examples to illustrate the calculations.
Formula to Determine Voltage
Voltage (\( V \)) can be calculated using the formula:
\[ V = \sqrt{P \cdot R} \]
where:
- \( V \) is the voltage (in volts, V),
- \( P \) is the power (in watts, W),
- \( R \) is the resistance (in ohms, \(\Omega\)).
Example 1: Voltage of a Lamp
Scenario: A lamp consumes \( 40 \, \text{W} \) of power and has a resistance of \( 360 \, \Omega \). What is the voltage across the lamp?
Step-by-Step Calculation:
1. Given:
\[ P = 40 \, \text{W} \]
\[ R = 360 \, \Omega \]
2. Substitute Values into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{40 \cdot 360} \]
3. Perform the Calculation:
\[ V = \sqrt{14400} \]
\[ V = 120 \, \text{V} \]
Final Value
The voltage across the lamp is:
\[ V = 120 \, \text{V} \]
Example 2: Voltage in a Toaster
Scenario: A toaster uses \( 750 \, \text{W} \) of power and has a resistance of \( 44 \, \Omega \). Find the voltage.
Step-by-Step Calculation:
1. Given:
\[ P = 750 \, \text{W} \]
\[ R = 44 \, \Omega \]
2. Substitute Values into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{750 \cdot 44} \]
3. Perform the Calculation:
\[ V = \sqrt{33000} \]
\[ V \approx 181.66 \, \text{V} \]
Final Value
The voltage in the toaster is approximately:
\[ V \approx 181.66 \, \text{V} \]
Example 3: Voltage of an Electric Kettle
Scenario: An electric kettle consumes \( 2000 \, \text{W} \) of power and has a resistance of \( 22 \, \Omega \). Calculate the voltage.
Step-by-Step Calculation:
1. Given:
\[ P = 2000 \, \text{W} \]
\[ R = 22 \, \Omega \]
2. Substitute Values into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{2000 \cdot 22} \]
3. Perform the Calculation:
\[ V = \sqrt{44000} \]
\[ V \approx 209.76 \, \text{V} \]
Final Value
The voltage of the electric kettle is approximately:
\[ V \approx 209.76 \, \text{V} \]
Summary
To find the voltage (\( V \)) given the power (\( P \)) and resistance (\( R \)), use the formula:
\[ V = \sqrt{P \cdot R} \]
In the examples provided:
1. A lamp consuming \( 40 \, \text{W} \) and \( 360 \, \Omega \) resistance has a voltage of \( 120 \, \text{V} \).
2. A toaster using \( 750 \, \text{W} \) and \( 44 \, \Omega \) resistance has a voltage of approximately \( 181.66 \, \text{V} \).
3. An electric kettle consuming \( 2000 \, \text{W} \) and \( 22 \, \Omega \) resistance has a voltage of approximately \( 209.76 \, \text{V} \).
