Ontological Layer: Material Opposition
Resistance & Conductance
The Physics of Opposition and Power Dissipation
The Friction of the Machine
Potential provides the push. Current is the flow. Resistance is the inevitable collision between moving charge and the atomic lattice. This territory formalizes how material properties and geometry dictate that opposition, translating kinetic electrical energy into heat, and defining the bounds of circuit efficiency.
MATERIAL →
RESISTIVITY (ρ) →
GEOMETRY (L/A) →
RESISTANCE (R) →
CURRENT RESPONSE →
POWER DISSIPATION
RECIPROCAL:
RESISTANCE →
CONDUCTANCE (G) |
RESISTIVITY →
CONDUCTIVITY (σ)
The 13 Resistance Concepts
Vertical Ontology: From Physics to Circuit Models
LEVEL 01
Electrical Resistance
- Physical Meaning of Resistance
- Opposition to Current Flow
- Electron-Lattice Collisions
- Ohm (Ω) Definition
Geometry & Resistivity
- Material Dependence (Resistivity ρ)
- Length of Conductor (L)
- Cross-sectional Area (A)
- Formula: R = ρ(L/A)
Conductance & Conductivity
- Conductance (G = 1/R) [Siemens]
- Conductivity (σ = 1/ρ)
- Ease of Current Flow
- Relationship to Material Quality
Temperature Effects
- Temperature Dependence
- Increased Lattice Vibration
- Temp Coefficient of Resistance (α)
- PTC vs NTC Materials
Linear vs Nonlinear
- Linear / Ohmic Resistance
- Nonlinear Resistance
- V-I Characteristic Curves
- Bridge to Semiconductor Devices
Static & Dynamic
- Static Resistance (R = V/I)
- Operating Point (Q-Point)
- Dynamic/Differential (r = dV/dI)
- AC vs DC Resistance Modeling
Resistance in Series
- End-to-End Connection
- Common Current Path
- Equivalent Resistance Addition
- Voltage Division Principle
Resistance in Parallel
- Shared Nodes (Common Voltage)
- Multiple Current Paths
- Conductance Addition (Geq = ΣG)
- Current Division Principle
Division Rules
- Voltage Division Rule (VDR)
- Current Division Rule (CDR)
- Proportional Distribution
- Circuit Simplification Tools
Open & Short Circuits
- Open Circuit (R → ∞, I = 0)
- Short Circuit (R → 0, V = 0)
- Fault Conditions
- Bypass & Infinite Resistance
Power Dissipation
- Joule Heating Effect
- Power Formulas (P = I²R = V²/R)
- Resistor Power Ratings
- Energy Loss in Transmission
Internal Resistance
- Practical Voltage Sources
- Internal Resistance (Rs)
- Voltage Drop Under Load
- Contact & Trace Resistance
Semiconductor Bridge
- From Macroscopic to Microscopic
- Conductivity (σ = n e μ)
- Charge Carrier Concentration
- Bridge to Realm 02: Semiconductors
SIMULATION RUNNING