Electrical Circuits and Components

• An electrical circuit is a closed path or loop through which electric charge flows.
• Typically consists of a voltage source, conductive wires, and electrical components
• Components include resistors, capacitors, and inductors.
• Electric charge flow is called electric current, measured in amperes (A)
• Circuits are fundamental to electronics and used in many applications.

Basic Circuit Components

• Voltage Source: Provides the electrical potential difference (voltage) that drives current flow, measured in volts (V).
• Resistor: Opposes current flow, dissipates energy as heat (measured in ohms, Ω).
• Capacitor: Stores electrical energy in an electric field (measured in farads, F).
• Inductor: Stores electrical energy in a magnetic field (measured in henries, H).
• Switch: Controls current flow by opening/closing the circuit.

Circuit Laws

• Ohm's Law: Voltage (V) across a resistor is proportional to current (I); V = IR.
• Kirchhoff's Current Law (KCL): Total current entering a junction equals the total current leaving.
• Kirchhoff's Voltage Law (KVL): The sum of voltage drops/rises around a closed loop is zero.

Series Circuits

• Components are connected end-to-end along a single path.
• Current is the same through all components.
• Total resistance is the sum of individual resistances: R_total = R_1 + R_2 + R_3 + ...
• Total voltage is divided among the components.

Parallel Circuits

• Components are connected across each other, providing multiple paths for current flow.
• Voltage is the same across all components.
• Total current is the sum of the currents through each component.
• The reciprocal of total resistance is the sum of reciprocals: 1/R_total = 1/R_1 + 1/R_2 + 1/R_3 + ...

Power in Electrical Circuits

• Electrical power (P) is the rate of energy transfer/consumption, measured in watts (W).
• P = VI, P = I^2R, and P = V^2/R are formulas to calculate power.
• Resistors dissipate power as heat; voltage sources supply power.

Circuit Analysis Techniques

• Series and Parallel Combination: Simplifies circuits by combining resistors to find equivalent resistances.
• Voltage Divider: A series circuit that produces a fraction of the source voltage; voltage is proportional to resistance.
• Current Divider: A parallel circuit that splits the total current; current is inversely proportional to resistance.
• Mesh Analysis (Loop Analysis): Solves for unknown currents using KVL in independent loops.
• Nodal Analysis: Solves for unknown voltages using KCL at each node.
• Superposition Theorem: Total current/voltage is the sum of the effects of each independent source.
• Thevenin's Theorem: Any linear circuit can be replaced by a voltage source (V_Th) in series with a resistor (R_Th).
• Norton's Theorem: Any linear circuit can be replaced by a current source (I_N) in parallel with a resistor (R_N).

Alternating Current (AC) Circuits

• Voltage and current vary sinusoidally.
• Frequency (f): Cycles per second, measured in hertz (Hz).
• Period (T): Time for one cycle; T = 1/f.
• AC voltage/current are described by root-mean-square (RMS) values.
• Reactance: Opposition to current due to capacitors/inductors.
• Capacitive reactance (X_C): Inversely proportional to frequency and capacitance; X_C = 1 / (2πfC).
• Inductive reactance (X_L): Directly proportional to frequency and inductance; X_L = 2πfL.
• Impedance (Z): Total opposition to current, combining resistance and reactance.
• Phase angle (φ): The phase difference between voltage and current.
• In a resistive circuit, voltage and current are in phase (φ = 0°).
• In a capacitive circuit, current leads voltage by 90° (φ = -90°).
• In an inductive circuit, voltage leads current by 90° (φ = 90°).

Series RLC Circuits

• Contains a resistor (R), inductor (L), and capacitor (C) in series.
• Impedance: Z = √(R^2 + (X_L - X_C)^2).
• Resonance: When X_L = X_C.
• At resonance, impedance is minimal (Z = R), current is maximal, and the phase angle is zero.
• Resonant frequency: f_0 = 1 / (2π√(LC)).

Parallel RLC circuits

• Contains a resistor (R), inductor (L), and capacitor (C) in parallel.
• At resonance, admittance is minimal, and impedance is maximal.
• Resonant frequency: f_0 = 1 / (2π√(LC)).

Transient Analysis

• Analysis of circuit behavior vs time, with switching or energy storage elements.
• Uses differential equations to find voltage and current.
• Important for switching behavior, and filter design

Circuit Simulation Software

• Used for circuit modeling and analysis, which aids in design and testing.
• Allows virtual breadboarding.
• Provides representations of circuit behavior, reducing the need for physical prototypes.