How To Find Electric Potential Using Power And Resistance

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

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, $\mathrm{\Omega }$)

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
• $R=24$ $\mathrm{\Omega }$

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
• $R=30$ $\mathrm{\Omega }$

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
• $R=20$ $\mathrm{\Omega }$

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.