To determine the electrical power (\( P \)) when current (\( I \)) and resistance (\( R \)) are known, use the formula:
\[ P = I^2 \cdot R \]
where:
- \( P \) is the power (in watts, W),
- \( I \) is the current (in amperes, A),
- \( R \) is the resistance (in ohms, Ω).
Problem 1: Power of a Resistor
Scenario: A resistor has a resistance of \( 10 \, \Omega \) and a current of \( 2 \, \text{A} \) flows through it. What is the power dissipated by the resistor?
Calculation:
1. Given:
\[ I = 2 \, \text{A} \]
\[ R = 10 \, \Omega \]
2. Substitute into the Power Formula:
\[ P = I^2 \cdot R \]
\[ P = (2)^2 \cdot 10 \]
3. Calculate:
\[ P = 4 \cdot 10 = 40 \, \text{W} \]
Answer: The power dissipated by the resistor is \( 40 \, \text{W} \).
Problem 2: Power of a Heating Element
Scenario: A heating element with a resistance of \( 50 \, \Omega \) has a current of \( 3 \, \text{A} \). Determine the power consumed by the heating element.
Calculation:
1. Given:
\[ I = 3 \, \text{A} \]
\[ R = 50 \, \Omega \]
2. Substitute into the Power Formula:
\[ P = I^2 \cdot R \]
\[ P = (3)^2 \cdot 50 \]
3. Calculate:
\[ P = 9 \cdot 50 = 450 \, \text{W} \]
Answer: The power consumed by the heating element is \( 450 \, \text{W} \).
Problem 3: Power in an Electric Motor
Scenario: An electric motor operates with a resistance of \( 20 \, \Omega \) and a current of \( 4 \, \text{A} \). What is the power output of the motor?
Calculation:
1. Given:
\[ I = 4 \, \text{A} \]
\[ R = 20 \, \Omega \]
2. Substitute into the Power Formula:
\[ P = I^2 \cdot R \]
\[ P = (4)^2 \cdot 20 \]
3. Calculate:
\[ P = 16 \cdot 20 = 320 \, \text{W} \]
Answer: The power output of the motor is \( 320 \, \text{W} \).
