9.3 Ohm’s Law and Kirchhoff’s Loop Rule (Resistors in Series and Parallel)

9.3 Ohm’s Law, Kirchhoff’s Loop Rule (Resistors in Series and Parallel)

As of 2021, the College Board tests only Units 1-7 on the AP Physics 1 exam. While this content will not be directly tested, it remains an excellent resource for mastering electrical circuit analysis.

Enduring Understanding 5.B

The energy of a system is conserved.

Essential Knowledge 5.B.9

Kirchhoff’s loop rule describes the conservation of energy in electrical circuits.

Kirchhoff’s Loop Rule Explained

Kirchhoff’s Loop Rule states that the sum of the potential differences (voltage drops and gains) around any closed loop in a circuit equals zero. This principle arises from the conservation of energy:

• The energy gained by the charge from the battery is fully transferred to the components in the circuit (resistors, capacitors, etc.).

• By the time the charge completes the loop and returns to the battery, all its energy has been used.

Key Concepts:

1. Voltage Drops:

   • The voltage drop across a resistor is the product of the current and the resistance.

   • Mathematically: .

2. Energy Transfer:

   • The rate of energy transfer in a resistor is given by: , where is power, is current, and is voltage.

3. Voltage Equality:

   • The total voltage drops across all components in a circuit equals the voltage supplied by the source.

Ohm’s Law

Ohm’s Law provides the foundational relationship between voltage, current, and resistance in a circuit:

Applications of Ohm’s Law:

1. Series Circuits:

   • The total resistance is the sum of individual resistances: .

   • The current remains the same through all components.

2. Parallel Circuits:

   • The total resistance is calculated using:

   • The voltage across each branch is the same, while the current divides among the branches.

Examples and Practical Applications

1. Analyzing a Simple Circuit:

   • Given a circuit with a 12V battery and two resistors in series, calculate:

     • Total resistance: .

     • Current: .

     • Voltage drop across : .

2. Kirchhoff’s Loop Rule in Action:

   • In a circuit with a 9V battery, a resistor, and an unknown resistor in parallel, calculate if the total current is 3A.

     • Voltage: .

     • Since is the same across all branches, use .

3. Energy Conservation in a Loop:

   • A 6V battery supplies energy to a circuit with a resistor and a motor requiring 2V. Verify energy conservation:

     • Voltage drop in resistor: .

     • Total voltage drop: , matching the source voltage.

Key Takeaways

• Kirchhoff’s Loop Rule and Ohm’s Law are essential for analyzing electrical circuits.

• Understanding resistors in series and parallel allows you to calculate voltage, current, and resistance accurately.

• These concepts underscore the principle of energy conservation, making them fundamental in both theoretical and practical applications.