Electrical Circuits

📐 Clausius-Mossotti

N ($10^{28}$/m³)

α ($10^{-40}$ F·m²)

Relative Permittivity $\varepsilon_r$: 1.45

🔬 Piezo Calculator

Stress T (MPa)

d-const (pC/N)

Polarization P: 2.0 μC/m²

🌡️ Pyro Calculator

ΔT (K)

λ (μC/m²K)

Change in P: 150 μC/m²

🌈 Refractive Index

Refractive Index (n)

Permittivity ε_r = n² : 2.25

🧪 Lorentz-Lorentz

Index (n)

Mol. Wt (M)

Density (ρ)

Molar Refraction R_m: 0.005

⚡ Townsend Breakdown

α (m⁻¹)

d (mm)

γ (coeff)

Criterion γ(e^αd - 1): 0.51

Safe (No Spark)

🔴 Liquid Globule

Surface Tension σ

Radius R (μm)

Permittivity ε_L

Critical E: 180.2 kV/cm

🌡️ Thermal Breakdown

Field E (kV/cm)

Freq f (Hz)

ε_r

tan δ

Heat W: 0.208 W/cm³

📉 Loss Tangent

ε' (Storage)

ε'' (Loss)

tan δ: 0.010

Q-Factor: 100

🌀 Debye Plotter

ε_s (Static)

ε_∞ (Opt)

τ (ns)

Peak Loss at: 159.2 MHz

📏 Dielectric Strength

Material E_bd (kV/cm)

Thickness d (mm)

Max Voltage V_max: 6.0 kV

🔋 Energy Loss

ω (rad/s)

ε_r

tan δ

E₀ (kV/m)

Loss W: 0.556 W/m³

📊 Material Selector

Min E_bd (kV/cm)

Max Op Temp (°C)

Recommended: Mica, Glass, Porcelain

🌡️ Class Finder

Operating Temp (°C)

Required: Class F (150°C)

⏳ Life Expectancy

Base Temp T₁ (°C)

Base Life L₁ (yrs)

New Temp T₂ (°C)

Predicted Life L₂: 10.00 yrs

💎 Crystal Calculator

Atomic Radius r (Å)

Structure

Lattice Parameter a: 3.51 Å

Effective Atoms N: 4

Packing Efficiency: 74%

🔍 Dielectric Identifier

Select Category

Non-Polar: Electronic only. (Diamond)

📑 Insulation Categories

Organic: Wood, Paper, Cotton, Rubber (Natural)
Inorganic: Glass, Mica, Ceramic, SF6 (Gaseous)
Synthetic: Plastic (PVC, PE), Bakelite, Nylon

🔁 Matrix Orthogonality

Verifying property: $[A][B]^T = 0$. This confirms KCL and KVL are independent layers of the same topology.

Incidence Matrix Column Sum: ✅ 0 (All branches)

🔄 Dual Mapper

Source Element

Dual element: Conductance (G)

⚛️ Atom Counter

Corners (1/8)

Faces (1/2)

Edges (1/4)

Body (1)

Total Atoms (N): 4

📐 APF Calculator

Structure Type

APF: 74% | Void: 26%

🔢 Lattice Parameter (a)

Radius r (Å)

Structure

a: 3.51 Å

🎯 Crystal Identifier

Coordination No.

Matches: FCC Structure

📊 Complete Comparison

Property	Diamond (dc)	SC	BCC	FCC
Atoms (N)	8	1	2	4
CN	4	6	8	12
r vs a	$a\sqrt{3}/8$	$a/2$	$a\sqrt{3}/4$	$a\sqrt{2}/4$
APF	34%	52%	68%	74%
Examples	Ge, Si, C	Po	Na, Li, Cr	Al, Cu, Ag

📐 Miller Indices

Intercept x

Intercept y

Intercept z

Indices: (1 1 0)

🔬 Bragg's Law

Order (n)

Spacing d (nm)

Angle θ (°)

Wavelength λ: 0.50 nm

🧲 Material Identifier

Property Selection

Classification: Diamagnetic

🌡️ Curie Temp Finder

Material

Tc = 770 °C (1043 K)

📈 Langevin L(α)

Atoms (N)

Temp T (K)

H Field

Magnetization: Linear Regime

⚖️ Soft vs Hard Magnet

Coercivity (A/m)

Type: Soft Magnetic (Transformer Core)

🔢 Unit Converter

Direction

Value

Result: 0.1 Tesla

Error Calculator

Measured Value (A_m)

True Value (A_t)

Click inputs to compute

Limiting Error Calculator

Full Scale (FSD)

Accuracy Class (%)

Reading (A_m)

Click inputs to compute

Error Propagation Calculator

Operation

A

delta A

B (or n)

delta B

Click inputs to compute

Full Statistics Calculator

Data points (comma-separated)

Press Compute to see results

Discover circuit

Module 1

Fundamental Concepts

Module 2

DC & AC Analysis

Module 3

Network Theorems

Module 4

Two Port Networks

Module 5

Electrical Materials