⚡Electrical Circuits and Systems I Unit 1 – Intro to Electrical Circuits

Key Concepts and Terminology

• Electrical circuits consist of interconnected components that allow the flow of electric current
• Voltage ($V$) represents the potential difference between two points in a circuit and is measured in volts
• Current ($I$) refers to the flow of electric charge through a circuit and is measured in amperes (amps)
• Resistance ($R$) opposes the flow of electric current in a circuit and is measured in ohms ($\Omega$)
• Ohm's Law states that the voltage across a resistor is directly proportional to the current flowing through it: $V = IR$
• Power ($P$) is the rate at which energy is transferred or consumed in a circuit and is measured in watts ($W$)
  • Calculated using the formula: $P = VI$
• Kirchhoff's Laws describe the behavior of current and voltage in a circuit
  • Kirchhoff's Current Law (KCL) states that the sum of currents entering a node equals the sum of currents leaving the node
  • Kirchhoff's Voltage Law (KVL) states that the sum of voltages around any closed loop in a circuit is zero

Basic Circuit Elements

• Resistors are passive components that oppose the flow of electric current and dissipate energy as heat
  • Resistors are used to control current, divide voltage, and provide electrical resistance in circuits
• Capacitors store electrical energy in an electric field and consist of two conductive plates separated by an insulator (dielectric)
  • Capacitance ($C$) is measured in farads ($F$) and represents the ability of a capacitor to store charge
• Inductors store electrical energy in a magnetic field and consist of a coil of wire
  • Inductance ($L$) is measured in henries ($H$) and represents the ability of an inductor to store energy in its magnetic field
• Voltage sources provide a constant voltage to a circuit and can be either independent (batteries) or dependent (controlled by another voltage or current)
• Current sources provide a constant current to a circuit and can be either independent or dependent
• Switches control the flow of current in a circuit by opening or closing a conductive path
• Transformers are used to step up or step down AC voltage levels and consist of two coupled coils (primary and secondary windings)

Circuit Analysis Techniques

• Node-voltage analysis is a method for determining the voltages at each node in a circuit using KCL
  • Involves assigning a reference node (ground) and writing KCL equations for each remaining node
• Mesh-current analysis is a method for determining the currents flowing through each mesh (loop) in a circuit using KVL
  • Involves assigning a current to each mesh and writing KVL equations for each mesh
• Superposition theorem states that the response of a linear circuit with multiple independent sources can be found by summing the responses caused by each source acting alone
  • Allows for the analysis of circuits with multiple sources by considering the effect of each source individually
• Thévenin's theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source and a series resistor
  • Simplifies complex circuits for analysis and design purposes
• Norton's theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source and a parallel resistor
  • Provides an alternative representation of a circuit, which can be useful in certain analysis situations

DC Circuit Analysis

• DC (direct current) circuits involve constant, unidirectional current flow and are powered by sources such as batteries or DC power supplies
• Series circuits have components connected end-to-end, forming a single path for current flow
  • In series circuits, the current is the same through all components, and the total voltage is the sum of the individual voltage drops
• Parallel circuits have components connected across the same two nodes, forming multiple paths for current flow
  • In parallel circuits, the voltage is the same across all components, and the total current is the sum of the individual branch currents
• Series-parallel circuits contain a combination of series and parallel connections
  • Analyzed by breaking the circuit into smaller series and parallel sections and applying the appropriate rules
• Voltage dividers are circuits that produce an output voltage that is a fraction of the input voltage
  • Consist of two resistors in series, with the output voltage taken across one of the resistors
• Current dividers are circuits that split the input current into two or more branch currents
  • Consist of two resistors in parallel, with each branch carrying a portion of the total current

AC Circuit Fundamentals

• AC (alternating current) circuits involve time-varying, sinusoidal current and voltage waveforms
  • AC is used in power distribution systems due to its ability to be easily transformed to higher or lower voltages
• AC waveforms are characterized by their amplitude, frequency, and phase
  • Amplitude represents the maximum value of the waveform (peak voltage or current)
  • Frequency ($f$) is the number of cycles per second and is measured in hertz ($Hz$)
  • Phase describes the relative timing between two waveforms and is measured in degrees or radians
• Phasors are complex numbers that represent the amplitude and phase of AC waveforms
  • Phasors simplify AC circuit analysis by allowing the use of complex arithmetic
• Impedance ($Z$) is the AC equivalent of resistance and represents the opposition to current flow in an AC circuit
  • Impedance is a complex quantity that includes both resistance and reactance (capacitive or inductive)
• Reactance is the opposition to current flow caused by capacitors (capacitive reactance, $X_C$) or inductors (inductive reactance, $X_L$) in AC circuits
  • Capacitive reactance decreases with increasing frequency, while inductive reactance increases with increasing frequency

Power in Electrical Circuits

• Instantaneous power is the product of the instantaneous voltage and current in a circuit
  • Represents the power at a specific moment in time
• Average power is the time-averaged value of the instantaneous power over one complete cycle
  • Represents the net power delivered to or consumed by a component
• Real power ($P$) is the average power consumed by resistive components in an AC circuit and is measured in watts ($W$)
  • Represents the useful work done by the circuit
• Reactive power ($Q$) is the average power exchanged between the source and reactive components (capacitors and inductors) in an AC circuit and is measured in volt-amperes reactive ($VAR$)
  • Represents the power that is stored and released by reactive components without doing useful work
• Apparent power ($S$) is the vector sum of real and reactive power in an AC circuit and is measured in volt-amperes ($VA$)
  • Represents the total power supplied by the source
• Power factor ($PF$) is the ratio of real power to apparent power in an AC circuit
  • Indicates the efficiency of power utilization in the circuit, with a higher power factor indicating more efficient power consumption

Circuit Theorems and Laws

• Maximum Power Transfer Theorem states that the maximum power is delivered to a load when the load resistance equals the source resistance
  • Helps in designing circuits for optimal power transfer efficiency
• Reciprocity Theorem states that in a linear, bilateral circuit, the voltage or current response in one branch due to a source in another branch is unchanged if the positions of the source and the response are interchanged
  • Useful in analyzing and simplifying complex circuits
• Substitution Theorem states that any element in a linear circuit can be replaced by a source and an impedance in series or parallel, provided that the source and impedance have the same voltage-current relationship as the original element
  • Allows for the simplification of circuits by replacing complex elements with equivalent sources and impedances
• Millman's Theorem provides a method for finding the voltage at a node in a circuit with multiple parallel branches, each containing a voltage source and a series impedance
  • Simplifies the analysis of circuits with multiple parallel voltage sources
• Tellegen's Theorem states that the sum of the powers consumed by all elements in a circuit is zero
  • Provides a general conservation law for electrical circuits and can be used to check the consistency of circuit analysis results

Practical Applications and Lab Work

• Breadboarding is a method for quickly prototyping and testing electronic circuits using a solderless breadboard
  • Allows for easy modification and troubleshooting of circuits during the design process
• Multimeters are instruments used to measure voltage, current, and resistance in electrical circuits
  • Essential tools for circuit analysis and troubleshooting
• Oscilloscopes are instruments used to display and analyze time-varying voltage and current waveforms
  • Particularly useful for visualizing and measuring AC signals and transient responses
• Simulation software (SPICE, Multisim) allows for the virtual design, analysis, and testing of electrical circuits
  • Enables rapid prototyping and optimization of circuits before physical implementation
• Printed Circuit Boards (PCBs) are used to mechanically support and electrically connect electronic components using conductive tracks, pads, and other features
  • Provide a permanent and reliable means of constructing electronic circuits for various applications
• Soldering is the process of joining electronic components to a PCB or other substrate using a melted metal alloy (solder)
  • Essential skill for assembling and repairing electronic circuits
• Troubleshooting techniques involve systematically identifying and isolating faults in electrical circuits
  • Includes visual inspection, continuity checks, voltage and current measurements, and signal tracing to pinpoint and resolve issues in malfunctioning circuits