To determine the resistance (\( R \)) when voltage (\( V \)) and power (\( P \)) are known, use the formula:
\[ R = \dfrac{V^2}{P} \]
where:
- \( R \) is the resistance (in ohms, Ω),
- \( V \) is the voltage (in volts, V),
- \( P \) is the power (in watts, W).
Problem 1: Resistance of a Lamp
Scenario: A lamp operates at \( 120 \, \text{V} \) and consumes \( 30 \, \text{W} \). What is the resistance of the lamp?
Calculation:
1. Given:
\[ V = 120 \, \text{V} \]
\[ P = 30 \, \text{W} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{(120)^2}{30} \]
3. Calculate:
\[ R = \dfrac{14400}{30} = 480 \, \Omega \]
Answer: The resistance of the lamp is \( 480 \, \Omega \).
Problem 2: Resistance in a Fan Motor
Scenario: A fan motor runs at \( 220 \, \text{V} \) and uses \( 110 \, \text{W} \). Determine the resistance.
Calculation:
1. Given:
\[ V = 220 \, \text{V} \]
\[ P = 110 \, \text{W} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{(220)^2}{110} \]
3. Calculate:
\[ R = \dfrac{48400}{110} = 440 \, \Omega \]
Answer: The resistance in the fan motor is \( 440 \, \Omega \).
Problem 3: Resistance of an Electric Stove
Scenario: An electric stove operates at \( 240 \, \text{V} \) and consumes \( 960 \, \text{W} \). What is the resistance?
Calculation:
1. Given:
\[ V = 240 \, \text{V} \]
\[ P = 960 \, \text{W} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V^2}{P} \]
\[ R = \dfrac{(240)^2}{960} \]
3. Calculate:
\[ R = \dfrac{57600}{960} = 60 \, \Omega \]
Answer: The resistance of the electric stove is \( 60 \, \Omega \).
