To determine the current (\( I \)) when voltage (\( V \)) and resistance (\( R \)) are known, use the formula:
\[ I = \dfrac{V}{R} \]
where:
- \( I \) is the current (in amperes, A),
- \( V \) is the voltage (in volts, V),
- \( R \) is the resistance (in ohms, Ω).
Problem 1: Current in a Wire
Scenario: A wire has a voltage of \( 24 \, \text{V} \) across it and a resistance of \( 6 \, \Omega \). What is the current through the wire?
Calculation:
1. Given:
\[ V = 24 \, \text{V} \]
\[ R = 6 \, \Omega \]
2. Substitute into the Current Formula:
\[ I = \dfrac{V}{R} \]
\[ I = \dfrac{24}{6} \]
3. Calculate:
\[ I = 4 \, \text{A} \]
Answer: The current through the wire is \( 4 \, \text{A} \).
Problem 2: Current Through a Resistor
Scenario: A resistor with \( 20 \, \Omega \) resistance is connected to a \( 40 \, \text{V} \) battery. What is the current flowing through the resistor?
Calculation:
1. Given:
\[ V = 40 \, \text{V} \]
\[ R = 20 \, \Omega \]
2. Substitute into the Current Formula:
\[ I = \dfrac{V}{R} \]
\[ I = \dfrac{40}{20} \]
3. Calculate:
\[ I = 2 \, \text{A} \]
Answer: The current flowing through the resistor is \( 2 \, \text{A} \).
Problem 3: Current in a Motor
Scenario: An electric motor operates at \( 120 \, \text{V} \) and has an internal resistance of \( 15 \, \Omega \). What is the current in the motor?
Calculation:
1. Given:
\[ V = 120 \, \text{V} \]
\[ R = 15 \, \Omega \]
2. Substitute into the Current Formula:
\[ I = \dfrac{V}{R} \]
\[ I = \dfrac{120}{15} \]
3. Calculate:
\[ I = 8 \, \text{A} \]
Answer: The current in the motor is \( 8 \, \text{A} \).
