Current Division Rule in Parallel Circuits

Course Information

• Course Title: Applied Electricity (EE 151)
• Instructor: Prof. Emmanuel Asuming Frimpong
• Address: Department of Electrical Engineering, KNUST, Kumasi, Ghana
• Email: [email protected]
• Phone: 0501349207/0246665284
• Office: Room 318
• Teaching Assistant: Sharon Amoah Mensah (NSP) - 0247994889
• Teaching Assistant: Andoh Buabeng Collins (ABC)

Course Aim

• To equip students with the tools to analyze electric and magnetic circuits.

Course Methodology

• Classroom lectures

Course Materials

• PowerPoint presentations
• Recommended textbooks:
  • E. Hughes, Electrical and Electronic Technology
  • P. Y. Okyere and E. A. Frimpong, Fundamentals of electric and magnetic circuits
  • S. N. Singh, Basic Electrical Engineering

Course Outline

• Unit 1: Circuits and Network Theorems: Kirchhoff's laws, Thevenin's Theorem, Norton's Theorem, Superposition Theorem, Reciprocity Theorem, and Delta-Star Transformation.
• Unit 2: Alternating Current Circuits: Determination of Average and RMS values, Harmonics, Phasors, impedance, current and power in AC circuits.
• Unit 3: Three-phase circuits: Connection of three-phase windings, three phase loads, power in three-phase circuits, solving three-phase circuit problems.
• Unit 4: Magnetic circuits: Components and terminologies, solving magnetic circuit problems

Lesson Plan

• Week 1: Chapter 1 – Course overview and DC circuit fundamentals
• Week 2: Chapter 1 – Course overview and DC circuit fundamentals
• Week 3: Chapter 1 - DC circuit fundamentals (cont.) and Kirchhoff's laws
• Week 4: Chapter 1 - Thevenin's theorem and Norton's theorem
• Week 5: Chapter 1 - Superposition theorem and Reciprocity theorem, Chapter 2 - Average value
• Week 6: Chapter 2 – RMS Harmonics, Phasors, and Impedance
• Week 7: Chapter 2 - Power in AC circuits and Application of complex numbers to AC circuits
• Week 8: Three-phase circuits
• Week 9: Three-phase circuits/Mag. cct
• Week 10: Magnetic circuits
• Week 11: Mid-semester examination
• Week 12: Mid-semester break
• Week 13: Revision
• Week 14: Revision
• Week 15: End-of-semester examination

Classroom Norms

• No phone usage
• No eating
• No noise-making
• No lateness
• No intimidation
• No sleeping
• Students who fail to abide by these norms will be asked to leave the classroom

Assessment

• Quizzes (30%)
• Mid-semester examination
• End of semester examination (70%)

Extras

• Daily admonishment and encouragement
• Random call-ups to ask and answer questions

Additional Material

• The course includes biblical quotes.

Circuit Terminologies

• Node (Junction): A point where currents split or come together
• Path: Any connection where current flows
• Branch: A connection between two nodes
• Loop/Mesh: A closed path of a circuit
• Short-circuit: A branch of theoretically zero resistance
• Open circuit: A branch of theoretically infinite resistance

Resistors in Series

• Resistors are in series when the same current flows through them.
• There is no junction between them.
• Total resistance (Rt) is the sum of the individual resistances, Rt=R₁ + R₂ +... + Rₙ

Resistors in Parallel

• Resistors are in parallel when the voltage across them is the same.
• Two resistors are in parallel if it is possible to traverse them without passing through another element.
• Total resistance (Rt) for two resistors R₁ and R₂ , 1/Rt = 1/R₁ + 1/R₂

Effective Resistance of a Circuit

• Effective circuit resistance is found by identifying and combining series and/or parallel resistors.

Current Division Rule

• The current division rule is applied to share current between parallel branches.
• Similar formulas exist for scenarios where multiple branches share a common current.

Voltage Drop

• Voltage drops across a resistor, and is proportional to the resistance and current..

Kirchhoff's Current Law (KCL)

• The sum of currents entering a node equals the sum of currents leaving the node.

Kirchhoff's Voltage Law (KVL)

• Sum of voltages in a closed loop (closed path) is zero.
• Algebraic summing of voltage sources in a loop equals the algebraic sum of voltage drops.

Thevenin's Theorem

• Any linear circuit connected between two terminals can be replaced by a Thevenin's voltage (VTH) in series with a Thevenin's resistance (RTH)
• VTH is the open-circuit voltage across the terminals.
• RTH is the resistance seen from the terminals when all sources are deactivated

Norton's Theorem

• Any linear circuit connected between two terminals can be replaced by a Norton's current(IN) in parallel with a Norton's resistance (RN).
• IN is the short-circuit current between the terminals
• RN is the resistance seen from the terminals when all sources are deactivated (RN = RTH)

Superposition Theorem

• Method to find current of/voltage across elements in a multiple-source linear circuit by summing the individual currents and voltages of individual sources acting alone.

Reciprocity Theorem

• Ideal ammeter and ideal voltage source interchanged in different branches of a linear network without changing the ammeter reading can be done.

Delta-Star Transformation

• Used in situations where neither series nor parallel arrangements can be identified.
• An arrangement of three (3) resistors where the resistors are connected to each other, arranged in a delta or star.

Alternating Current (AC) Circuits

• AC circuits deal with time-varying voltages and currents.
• Sine, square, and triangular waves are examples of AC waveforms.
• Characteristics of AC waveforms include: amplitude (peak), cycle, period, and frequency.

Average Value

• The average value of a periodic function is its dc value.
• Method to obtain the average value of a waveform includes identifying its cycle, noting its period, finding the area of the cycle, and then dividing by its period.

Root Mean Square (RMS) Value

• The effective value of an AC waveform.
• Method for determining the RMS value includes squaring the waveform, integrating the squared area over time, dividing by the period, and taking the square root of the result.

Harmonics

• Non-sinusoidal periodic voltages and currents as expressed as the sum of sine waves, with multiple frequencies all multiples of a fundamental frequency.

Phasors

• Represent sinusoidal quantities to make analysis easier.
• A straight line whose length is proportional to the rms value of the voltage or current, with arrow indicating phase angle or phase difference.

Phasor Diagrams

• Diagram using phasors to analyze AC quantities, including quantities and phase relations in a circuit.

Addition and Subtraction of Sinusoidal Quantities

• Adding sinusoidal quantities based on their phasor representations.
• Subtracting sinusoidal quantities by reversing the subtracted quantity's component and adding as a vector to the other quantity.

Three-Phase Circuits

• Circuits using three separate sinusoidal voltages that are 120 degrees out of phase with each other.
• Three-phase analysis often involves determining phase and line currents and voltages, power factors, and total power.

Calculation of Complex Power

• Solving AC circuit problems by treating relevant quantities as complex numbers.