To determine the voltage (\( V \)) when current (\( I \)) and resistance (\( R \)) are known, use the formula:
\[ V = I \cdot R \]
where:
- \( V \) is the voltage (in volts, V),
- \( I \) is the current (in amperes, A),
- \( R \) is the resistance (in ohms, Ω).
Problem 1: Voltage Across a Resistor
Scenario: A circuit has a resistor with \( 10 \, \Omega \) resistance and a current of \( 2 \, \text{A} \) flowing through it. What is the voltage across the resistor?
Calculation:
1. Given:
\[ I = 2 \, \text{A} \]
\[ R = 10 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = I \cdot R \]
\[ V = 2 \cdot 10 \]
3. Calculate:
\[ V = 20 \, \text{V} \]
Answer: The voltage across the resistor is \( 20 \, \text{V} \).
Problem 2: Voltage in a Light Bulb
Scenario: A light bulb has a resistance of \( 30 \, \Omega \) and a current of \( 0.5 \, \text{A} \). What is the voltage required to operate the bulb?
Calculation:
1. Given:
\[ I = 0.5 \, \text{A} \]
\[ R = 30 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = I \cdot R \]
\[ V = 0.5 \cdot 30 \]
3. Calculate:
\[ V = 15 \, \text{V} \]
Answer: The voltage required is \( 15 \, \text{V} \).
Problem 3: Voltage for a Heater
Scenario: An electric heater has a resistance of \( 50 \, \Omega \) and draws a current of \( 3 \, \text{A} \). Find the voltage applied to the heater.
Calculation:
1. Given:
\[ I = 3 \, \text{A} \]
\[ R = 50 \, \Omega \]
2. Substitute into the Voltage Formula:
\[ V = I \cdot R \]
\[ V = 3 \cdot 50 \]
3. Calculate:
\[ V = 150 \, \text{V} \]
Answer: The voltage applied to the heater is \( 150 \, \text{V} \).
