Circuit Analysis I - Series and Parallel Circuits

Learning Outcomes

• Understand the behavior of resistors in series and parallel configurations.
• Analyze series-parallel circuits effectively.
• Explain and calculate the loaded voltage divider output.

Introduction to Series and Parallel Circuits

• Basic Circuit Elements: Simple circuits usually consist of a single battery and load resistance but practical circuits often involve multiple connected components.
• Series Circuits:
  • Components are connected end-to-end, forming a single path for current flow.
  • The same current flows through all components.

Characteristics of Parallel Circuits

• Parallel Connections:
  • Components are connected across each other's leads.
  • Multiple paths for current flow exist, but the voltage remains the same across components.

Series-Parallel Combinations

• Complex Configurations:
  • Circuits can consist of both series and parallel connections.
  • Different rules need to be applied selectively based on the section of the circuit being analyzed.

Steps for Analyzing Series-Parallel Circuits

1. Identify Connections: Determine which resistors are in series or parallel.
2. Redraw the Circuit: Simplify the circuit by replacing identified series or parallel combinations with equivalent resistors.
3. Repeat the Process: Continue simplifying until only one equivalent resistor remains.
4. Calculate Total Current: Use the total voltage and resistance: I = \frac{V}{R}.
5. Insert Values: Go back to the simplified circuit with known voltage and current values.
6. Apply Ohm's Law: Calculate unknown values using V = IR or I = \frac{V}{R}.
7. Iterate: Repeat until all voltage and current values are determined in the original circuit.
8. Calculate Power Dissipation: Use known values of voltage, current, and resistance to find power losses in the circuit.

Example of Series-Parallel Circuit Analysis

• Example: Identify how resistors are connected in the provided circuit.
• For instance, if resistors R1 and R2 in series are combined with R3 in parallel, identify relationships and use respective formulas to calculate total resistance (RT).

Voltage Source and Current Paths

• Current Division: Total current entering a junction divides into multiple paths if resistors are in parallel.
• Comparative Situations: Understanding the voltage drop across various resistors and their relationships in more complex circuits.

Loaded Voltage Divider

• Voltage Divider Basics: A loaded voltage divider consists of resistors connected in series with a load resistor in parallel with one of them.
• The output voltage across the load can be affected by the load's resistance:
  • Voltage Divider Equation: V{OUT} = V{S} \cdot \frac{R{2}}{R{1} + R_{2}}
• Loaded and Unloaded Outputs: Understand the difference in outputs based on whether a load resistor is connected.

Practical Application

• Familiarize yourself with solving circuit problems:
  • Use current and voltage laws, and divider equations to simplify analysis of complex circuits.

Questions and Further Exploration

• Maximize understanding by applying concepts to practice problems; solutions often require iterative approaches and logical analyses.

Summary

• Series and parallel circuits form the foundation of electrical analysis.
• Mastery of Ohm’s Law and circuit reduction techniques is crucial for electrical engineering problem-solving.
• The loaded voltage divider exemplifies the nuances of real-world circuit behavior.