To determine the resistance (\( R \)) when voltage (\( V \)) and current (\( I \)) are known, use the formula:
\[ R = \dfrac{V}{I} \]
where:
- \( R \) is the resistance (in ohms, Ω),
- \( V \) is the voltage (in volts, V),
- \( I \) is the current (in amperes, A).
Problem 1: Resistance of a Light Bulb
Scenario: A light bulb operates at \( 120 \, \text{V} \) and draws \( 0.5 \, \text{A} \) of current. What is the resistance of the bulb?
Calculation:
1. Given:
\[ V = 120 \, \text{V} \]
\[ I = 0.5 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V}{I} \]
\[ R = \dfrac{120}{0.5} \]
3. Calculate:
\[ R = 240 \, \Omega \]
Answer: The resistance of the light bulb is \( 240 \, \Omega \).
Problem 2: Resistance of a Heating Element
Scenario: A heating element has a voltage of \( 240 \, \text{V} \) across it and a current of \( 10 \, \text{A} \). What is the resistance?
Calculation:
1. Given:
\[ V = 240 \, \text{V} \]
\[ I = 10 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V}{I} \]
\[ R = \dfrac{240}{10} \]
3. Calculate:
\[ R = 24 \, \Omega \]
Answer: The resistance of the heating element is \( 24 \, \Omega \).
Problem 3: Resistance of an Electric Kettle
Scenario: An electric kettle operates at \( 220 \, \text{V} \) and uses \( 5 \, \text{A} \) of current. What is the resistance of the kettle's heating element?
Calculation:
1. Given:
\[ V = 220 \, \text{V} \]
\[ I = 5 \, \text{A} \]
2. Substitute into the Resistance Formula:
\[ R = \dfrac{V}{I} \]
\[ R = \dfrac{220}{5} \]
3. Calculate:
\[ R = 44 \, \Omega \]
Answer: The resistance of the electric kettle's heating element is \( 44 \, \Omega \).
