Applied Electricity - Introduction (Resistors in series and parallel, Delta-star)

Introduction

This tutorial will guide you through the fundamental concepts of applied electricity, specifically focusing on resistors in series and parallel configurations. Understanding these concepts is essential for analyzing electrical circuits, and you'll also learn about Kirchhoff's Voltage Law (KVL). By the end, you'll have a solid foundation to apply these principles in real-world electrical systems.

Step 1: Understanding Resistors in Series

Resistors are components that impede the flow of electric current. When connected in series, the total resistance can be calculated easily.

Key Points:

• The total resistance (R_total) in a series circuit is the sum of all individual resistances.
• Formula: R_total = R1 + R2 + R3 + ... + Rn

Practical Advice:

• Ensure that all resistors are connected end-to-end, forming a single path for current to flow.
• Remember that the current (I) remains constant through each resistor in a series.

Example Calculation:

• If you have three resistors with values of 2Ω, 3Ω, and 5Ω:
  • R_total = 2Ω + 3Ω + 5Ω = 10Ω

Step 2: Understanding Resistors in Parallel

Parallel circuits allow multiple paths for current to flow, which affects the total resistance differently than series.

Key Points:

• The total resistance in a parallel circuit is calculated using the reciprocal of the sum of the reciprocals of each individual resistance.
• Formula: 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn

Practical Advice:

• Ensure that all resistors are connected to the same two nodes, creating multiple pathways for the current.
• The voltage (V) across each resistor is the same in a parallel circuit.

Example Calculation:

• For resistors of 2Ω, 3Ω, and 6Ω in parallel:
  • 1/R_total = 1/2 + 1/3 + 1/6
  • 1/R_total = 3/6 + 2/6 + 1/6 = 6/6
  • R_total = 1Ω

Step 3: Applying Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltage) around any closed network is zero.

Key Points:

• KVL helps in analyzing complex circuits by ensuring that the total voltage supplied equals the total voltage drop across components.
• In a loop, the sum of voltage rises (sources) minus the sum of voltage drops (resistors) equals zero.

Practical Advice:

• Label voltages and resistances in your circuit diagram to apply KVL effectively.
• If the circuit has multiple loops, apply KVL to each loop independently for clarity.

Example Application:

• If you have a circuit with a 12V battery and resistors that drop 4V and 8V, KVL states:
  • 12V - 4V - 8V = 0

Conclusion

By understanding resistors in series and parallel configurations, as well as Kirchhoff's Voltage Law, you are now equipped to analyze and calculate circuit behavior effectively. These concepts are crucial for anyone studying or working with electrical systems. For further exploration, consider applying these principles to more complex circuits or experimenting with real-world electrical projects.