Lesson 2

DC Circuits

Introduction

• Course Title: Electrical Power E234

• Purpose: Electrical and Electronic Fundamentals for training purposes

• Modules:

  • Module 3: Electrical Fundamentals

  • Module 4: Electronic Fundamentals

Learning Outcomes

• Describe the relationship for current, resistance, and voltage in a simple DC circuit.

• Explain the two Kirchhoff's Circuit Laws.

• Explain power dissipation in DC circuits.

• Calculate the current and electrical power of DC circuits.

Power Sources

• Types of Power Sources:

  • Voltage Source: Maintains voltage at a constant level (64V DC in today's problem); does not change voltage based on load current.

  • Current Source: Supplies a constant current flow regardless of the voltage across its terminals.

• Electromotive Force (emf): Another term for the voltage generated by a power source.

Circuit Terminology

• Nodes: Points where two or more circuit elements meet.

• Branches: Components of the circuit connected between nodes.

• Loops: Closed paths through which current can circulate.

Law of Conservation of Energy

• Definition: Energy cannot be created or destroyed; it may change forms, but the total amount remains constant.

Kirchhoff's Circuit Laws

Kirchhoff's Current Law (KCL)

• Statement: The total current entering a node is equal to the total current leaving the node (conservation of charge).

• Formula:
  $I<em>{in1} + I</em>{in2} + I<em>{in3} + \u2026 = I</em>{out1} + I<em>{out2} + I</em>{out3} + <br>$

• Example:
  For node A:
  $20 = 3 + I<em>{2} + 12$ Therefore, $I</em>{2} = 20 - 15 = 5 mA$

Current Divider Rule

• Voltage at Node: The voltage remains the same at node A despite different branch currents.

• Formula:
  R{eq} = rac{1}{ rac{1}{R{1}} + rac{1}{R_{2}} +
  }

• Relation to Parallel Circuit: Current flowing through resistors in parallel can be expressed as follows:
  $I<em>{R1} = rac{V</em>{A}}{R<em>{1}} = rac{I</em>{S} imes R<em>{eq}}{R</em>{1}}$

Kirchhoff's Voltage Law (KVL)

• Statement: The algebraic sum of all voltages in a closed loop equals zero (conservation of energy).

• Formula:
  $ext{sum of voltage rises} = ext{sum of voltage drops}$

• Example:
  $ext{Vs} - V<em>{1} - V</em>{2} - V_{3} = 0$

Voltage Divider Rule

• Purpose: To find the voltage across a specific resistor in a series circuit.

• Formula:
  $V<em>{x} = rac{R</em>{x}}{R<em>{eq}} imes V</em>{s}$

• Example: For resistors R1, R2, R3 in series:
  $V<em>{R1} = rac{R</em>{1}}{R<em>{1}+R</em>{2}+R<em>{3}} imes V</em>{s}$

Power

• Definition of Energy: Ability to do work, measured in Joules (J).

• Definition of Power: Rate at which energy is consumed, measured in Watts (W).

  • Example: A light bulb rated at 15 Watts consumes 15 Joules per second.

• Power Calculation Formula:
  $P = rac{W}{t}$
  Where W is energy (in Joules) and t is time (in seconds).

• Electrical Power Formulas:

  • $P = VI$

  • $P = V^2 / R$

  • $P = I^2 R$

Power in Circuits

• Series Circuit: Total power consumed equals the sum of power dissipated by resistors:
  PT = P1 + P2 +  + Pn

• Parallel Circuit: Power consumed also equals the sum of power dissipated:
  $P<em>T = P</em>1 + P<em>2 + P</em>n$

Power Rating of Resistors

• Importance of Power Rating: Indicates how much power a resistor can handle without being damaged.

• Standard Ratings: 1W, 1/2W, 1/4W, 1/8W.

Example Calculations

• Calculate voltages using voltage divider and Kirchhoff's laws, power rating in circuits, and energy consumption based on the power rating over a specific duration.

• Energy Consumption Calculation: Multiply calculated power by operational duration (e.g., 24 hours).

Activities

• Activity 1: Apply Kirchhoff’s Laws in given scenarios (YouTube links provided for further explanation).

• Activity 2A & 2B: Calculate voltage, current, power across loads, and analyze changes when voltage is varied.

Summary

• Described the relationships in a simple DC circuit, explained Kirchhoff's Circuit Laws, discussed power dissipation in DC circuits, and calculated current and electrical power.

Lab Safety Regulations

• Requirements: All students must read updated safety handouts and acknowledge understanding by their lab instructor before attending lab sessions.