To determine the resistance (\( R \)) when power (\( P \)) and current (\( I \)) are known, use the formula:
\[ R = \dfrac{P}{I^2} \]
where:
- \( R \) is the resistance (in ohms, Ω),
- \( P \) is the power (in watts, W),
- \( I \) is the current (in amperes, A).
Problem 1: Resistance of a Heating Coil
Scenario: A heating coil consumes \( 200 \, \text{W} \) of power and has a current of \( 2 \, \text{A} \). What is the resistance of the coil?
Calculation:
1. Given:
\[ P = 200 \, \text{W} \]
\[ I = 2 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{P}{I^2} \]
\[ R = \dfrac{200}{(2)^2} \]
3. Calculate:
\[ R = \dfrac{200}{4} = 50 \, \Omega \]
Answer: The resistance of the heating coil is \( 50 \, \Omega \).
Problem 2: Resistance of a Power Resistor
Scenario: A power resistor dissipates \( 500 \, \text{W} \) and has a current of \( 5 \, \text{A} \). Determine the resistance.
Calculation:
1. Given:
\[ P = 500 \, \text{W} \]
\[ I = 5 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{P}{I^2} \]
\[ R = \dfrac{500}{(5)^2} \]
3. Calculate:
\[ R = \dfrac{500}{25} = 20 \, \Omega \]
Answer: The resistance of the power resistor is \( 20 \, \Omega \).
Problem 3: Resistance of an Electric Stove
Scenario: An electric stove operates at \( 900 \, \text{W} \) of power with a current of \( 6 \, \text{A} \). What is the resistance?
Calculation:
1. Given:
\[ P = 900 \, \text{W} \]
\[ I = 6 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{P}{I^2} \]
\[ R = \dfrac{900}{(6)^2} \]
3. Calculate:
\[ R = \dfrac{900}{36} = 25 \, \Omega \]
Answer: The resistance of the electric stove is \( 25 \, \Omega \).
