Circuit Analysis Basics

Circuit Analysis

Definition: The process of studying electrical circuits to determine voltage, current, and resistance in each component.
Basic Components:
- Resistor (R): Limits current; measured in Ohms (Ω).
- Capacitor (C): Stores electrical energy; measured in Farads (F).
- Inductor (L): Stores energy in a magnetic field; measured in Henrys (H).
- Voltage Source (V): Provides electrical potential; examples include batteries.
- Current Source (I): Provides constant current.
Ohm's Law:
- Formula: V = I × R
  - V = Voltage (Volts)
  - I = Current (Amperes)
  - R = Resistance (Ohms)
Kirchhoff's Laws:
- Kirchhoff's Current Law (KCL): The total current entering a junction equals the total current leaving.
- Kirchhoff's Voltage Law (KVL): The sum of all voltages around a closed loop equals zero.
Series and Parallel Circuits:
- Series Circuit:
  - Components connected end-to-end.
  - Total Resistance: R_total = R1 + R2 + ... + Rn
  - Voltage divides; current is constant.
- Parallel Circuit:
  - Components connected across the same two points.
  - Total Resistance: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn
  - Current divides; voltage is constant.
Thevenin's Theorem:
- Simplifies a complex circuit into a single voltage source (V_th) and a single resistor (R_th).
Norton's Theorem:
- Similar to Thevenin's but replaces the voltage source with a current source (I_no) and a parallel resistor (R_no).
AC vs. DC Circuits:
- AC (Alternating Current): Changes direction periodically. Characterized by frequency (Hz) and amplitude.
- DC (Direct Current): Flows in one direction. Constant voltage and current values.
Phasors:
- A mathematical representation of AC voltages and currents, expressed in terms of magnitude and phase angle.
Power in Circuits:
- Active Power (P): Actual power consumed, measured in Watts (W).
- Reactive Power (Q): Power stored and released, measured in Volt-Amperes Reactive (VAR).
- Apparent Power (S): The product of voltage and current; S = V × I (measured in Volt-Amperes, VA).
Transient Analysis:
- Studies circuits' behavior during changes in voltage or current.
- Includes first-order (RC, RL) and second-order (RLC) circuits.

These concepts form the foundation of circuit analysis in electrical and electronics engineering, aiding in system design, troubleshooting, and understanding complex circuits.

Circuit Analysis

Circuit Analysis is the examination of electrical circuits to determine voltage, current, and resistance within each component.
Essential Circuit Components:
- A Resistor (R) limits current flow. Measured in Ohms (Ω).
- A Capacitor (C) stores electrical energy. Measured in Farads (F).
- An Inductor (L) stores energy in a magnetic field. Measured in Henrys (H).
- A Voltage Source (V) provides electrical potential, like a battery.
- A Current Source (I) provides a constant current.
Ohm's Law describes the relationship between voltage, current, and resistance:
- V = I × R:
  - V is Voltage in Volts
  - I is Current in Amperes
  - R is Resistance in Ohms
Kirchhoff's Circuit Laws are fundamental principles for analyzing circuits:
- Kirchhoff's Current Law (KCL) states that the sum of currents entering a junction equals the sum of currents leaving.
- Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop equals zero.
Types of Circuits:
- Series Circuits:
  - Components are connected end-to-end.
  - Total Resistance (R_total) is the sum of individual resistances (R1 + R2 +...+ Rn).
  - Voltage is divided among components, while current remains constant.
- Parallel Circuits:
  - Components are connected across the same two points.
  - Total Resistance (R_total) is calculated as 1/R_total = 1/R1 + 1/R2 +...+ 1/Rn.
  - Current is divided among components, while voltage remains constant.
Thevenin's Theorem simplifies complex circuits into a single voltage source (V_th) and a single resistor (R_th).
Norton's Theorem similarly simplifies circuits, using a current source (I_no) and a parallel resistor (R_no) instead of a voltage source.
AC (Alternating Current) vs. DC (Direct Current) Circuits:
- AC Circuits have current that changes direction periodically, with frequency (Hz) and amplitude.
- DC Circuits have current flowing in one direction, with constant voltage and current values.
Phasors represent AC voltages and currents mathematically, showing magnitude and phase angle.
Power in Circuits:
- Active Power (P) is the actual power consumed, measured in Watts (W).
- Reactive Power (Q) is the power stored and released, measured in Volt-Amperes Reactive (VAR).
- Apparent Power (S) is the product of voltage and current, measured in Volt-Amperes (VA).
Transient Analysis studies how circuits behave during voltage or current changes.
- Includes first-order circuits (RC, RL) and second-order circuits (RLC).
These principles provide a foundation for circuit analysis in electrical and electronics engineering, assisting in system design, troubleshooting, and understanding complex circuits.