Circuit Analysis Basics

Circuit Analysis

Basics

• A circuit is a path through which electric current flows
• Consists of conductors (wires), resistors, capacitors, inductors, and power sources
• Can be classified into series, parallel, and series-parallel circuits

Kirchhoff's Laws

• Kirchhoff's Voltage Law (KVL)
  • The sum of voltage changes around a closed loop is zero
  • ∑ΔV = 0
• Kirchhoff's Current Law (KCL)
  • The sum of currents entering a node is equal to the sum of currents leaving a node
  • ∑I_in = ∑I_out

Circuit Analysis Techniques

• Node Analysis
  • Analyze a circuit by finding the voltage at each node
  • Uses KCL and Ohm's Law
• Mesh Analysis
  • Analyze a circuit by finding the current in each mesh
  • Uses KVL and Ohm's Law

Resistivity

Definition

• Resistivity (ρ) is the measure of how much a material resists the flow of electric current
• Unit: ohm-meters (Ωm)

Factors Affecting Resistivity

• Temperature
  • Resistivity increases with temperature in metals
  • Resistivity decreases with temperature in semiconductors
• Material
  • Different materials have different resistivities
  • Copper has a low resistivity, while rubber has a high resistivity

Applications

• Electrical Wiring
  • Low-resistivity materials (e.g. copper) are used to minimize energy loss
• Heating Elements
  • High-resistivity materials (e.g. nichrome) are used to convert electrical energy into heat

Circuit Analysis

Basics of Circuits

• A circuit is a path through which electric current flows
• Consists of conductors, resistors, capacitors, inductors, and power sources
• Classified into series, parallel, and series-parallel circuits

Kirchhoff's Laws

Kirchhoff's Voltage Law (KVL)

• Sum of voltage changes around a closed loop is zero
• Represented by the equation ∑ΔV = 0

Kirchhoff's Current Law (KCL)

• Sum of currents entering a node is equal to the sum of currents leaving a node
• Represented by the equation ∑I_in = ∑I_out

Analysis Techniques

Node Analysis

• Analyze a circuit by finding the voltage at each node
• Uses Kirchhoff's Current Law (KCL) and Ohm's Law

Mesh Analysis

• Analyze a circuit by finding the current in each mesh
• Uses Kirchhoff's Voltage Law (KVL) and Ohm's Law

Resistivity

Definition and Unit

• Resistivity (ρ) is the measure of how much a material resists the flow of electric current
• Unit: ohm-meters (Ωm)

Factors Affecting Resistivity

Temperature

• Resistivity increases with temperature in metals
• Resistivity decreases with temperature in semiconductors

Material

• Different materials have different resistivities
• Copper has a low resistivity, while rubber has a high resistivity

Applications of Resistivity

Electrical Wiring

• Low-resistivity materials (e.g. copper) are used to minimize energy loss

Heating Elements

• High-resistivity materials (e.g. nichrome) are used to convert electrical energy into heat

Learn the fundamentals of circuit analysis, including the definition of a circuit, types of circuits, and Kirchhoff's laws. Understand how to apply KVL and KCL to analyze circuits.