Calculating the electric potential (voltage) when the power and resistance are known is crucial in many electrical applications. The relationship between these quantities can be expressed using a specific formula and algebraic manipulation.
The Formula: \( P = \dfrac{V^2}{R} \)
To find the electric potential, we rearrange the formula as follows:
\[ V = \sqrt{P \cdot R} \]
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: Voltage for an Electric Kettle
Question: An electric kettle has a power rating of 2000 watts and a resistance of 24 ohms. What is the operating voltage of the kettle?
Calculation:
Given:
- \( P = 2000 \) W
- \( R = 24 \) \(\Omega\)
Using the formula:
\[ V = \sqrt{P \cdot R} = \sqrt{2000 \cdot 24} = \sqrt{48000} \approx 219 \, \text{V} \]
Result: The operating voltage of the electric kettle is approximately 219 volts.
Example 2: Voltage for a Space Heater
Question: A space heater consumes 1500 watts of power and has a resistance of 30 ohms. What is the voltage supply to the heater?
Calculation:
Given:
- \( P = 1500 \) W
- \( R = 30 \) \(\Omega\)
Using the formula:
\[ V = \sqrt{P \cdot R} = \sqrt{1500 \cdot 30} = \sqrt{45000} \approx 212 \, \text{V} \]
Result: The voltage supply to the space heater is approximately 212 volts.
Example 3: Voltage for an Electric Stove
Question: An electric stove operates with a power of 2500 watts and a resistance of 20 ohms. What is the required voltage?
Calculation:
Given:
- \( P = 2500 \) W
- \( R = 20 \) \(\Omega\)
Using the formula:
\[ V = \sqrt{P \cdot R} = \sqrt{2500 \cdot 20} = \sqrt{50000} \approx 224 \, \text{V} \]
Result: The required voltage for the electric stove is approximately 224 volts.
