To determine the voltage (\( V \)) when power (\( P \)) and resistance (\( R \)) are known, use 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, Ω).
Problem 1: Voltage Across a Resistor
Scenario: A resistor dissipates \( 25 \, \text{W} \) of power and has a resistance of \( 100 \, \Omega \). What is the voltage across the resistor?
Calculation:
1. Given:
\[ P = 25 \, \text{W} \]
\[ R = 100 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{25 \cdot 100} \]
3. Calculate:
\[ V = \sqrt{2500} = 50 \, \text{V} \]
Answer: The voltage across the resistor is \( 50 \, \text{V} \).
Problem 2: Voltage of a Power Supply
Scenario: A power supply provides \( 500 \, \text{W} \) to a circuit with a resistance of \( 200 \, \Omega \). Determine the voltage of the power supply.
Calculation:
1. Given:
\[ P = 500 \, \text{W} \]
\[ R = 200 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{500 \cdot 200} \]
3. Calculate:
\[ V = \sqrt{100000} = 316.23 \, \text{V} \]
Answer: The voltage of the power supply is approximately \( 316.23 \, \text{V} \).
Problem 3: Voltage in an Electric Appliance
Scenario: An electric appliance uses \( 3000 \, \text{W} \) of power and has a resistance of \( 75 \, \Omega \). What is the operating voltage?
Calculation:
1. Given:
\[ P = 3000 \, \text{W} \]
\[ R = 75 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = \sqrt{P \cdot R} \]
\[ V = \sqrt{3000 \cdot 75} \]
3. Calculate:
\[ V = \sqrt{225000} = 474.34 \, \text{V} \]
Answer: The operating voltage is approximately \( 474.34 \, \text{V} \).
