🌌Fundamental Constants
Speed of light in vacuum
\(c = 299\,792\,458\) m/s
Exact definition
Planck constant
\(h = 6.626\,070\,15 \times 10^{-34}\) J·s
Exact definition
Reduced Planck constant
\(\hbar = \frac{h}{2\pi} = 1.054\,571\,817 \times 10^{-34}\) J·s
ℏ = h/2π
Gravitational constant
\(G = 6.674\,30 \times 10^{-11}\) m³·kg⁻¹·s⁻²
Avogadro constant
\(N_A = 6.022\,140\,76 \times 10^{23}\) mol⁻¹
Exact definition
Boltzmann constant
\(k_B = 1.380\,649 \times 10^{-23}\) J/K
Exact definition
⚡Electromagnetic Constants
Fundamental Electromagnetic Constants
Elementary charge
\(e = 1.602\,176\,634 \times 10^{-19}\) C
Exact definition
Vacuum permittivity
\(\varepsilon_0 = 8.854\,187\,8128 \times 10^{-12}\) F/m
Electric constant
Vacuum permeability
\(\mu_0 = 4\pi \times 10^{-7}\) H/m
≈ 1.256637×10⁻⁶ H/m (exact)
Characteristic impedance of vacuum
\(Z_0 = \sqrt{\frac{\mu_0}{\varepsilon_0}} \approx 376.730\) Ω
Free space impedance
Magnetic flux quantum
\(\Phi_0 = \frac{h}{2e} = 2.067\,833\,848 \times 10^{-15}\) Wb
Josephson constant
\(K_J = \frac{2e}{h} = 483\,597.848\,4 \times 10^9\) Hz/V
von Klitzing constant
\(R_K = \frac{h}{e^2} = 25\,812.807\,45\) Ω
Quantum Hall resistance
Conductance quantum
\(G_0 = \frac{2e^2}{h} = 7.748\,091\,729 \times 10^{-5}\) S
Bohr magneton
\(\mu_B = \frac{e\hbar}{2m_e} = 9.274\,010\,08 \times 10^{-24}\) J/T
Nuclear magneton
\(\mu_N = \frac{e\hbar}{2m_p} = 5.050\,783\,75 \times 10^{-27}\) J/T
💡 Key Relationship
\(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\) - The speed of light is related to the electromagnetic properties of vacuum.
⚛️Atomic & Quantum Constants
Electron mass
\(m_e = 9.109\,383\,70 \times 10^{-31}\) kg
≈ 0.511 MeV/c²
Proton mass
\(m_p = 1.672\,621\,924 \times 10^{-27}\) kg
≈ 938.272 MeV/c²
Neutron mass
\(m_n = 1.674\,927\,498 \times 10^{-27}\) kg
≈ 939.565 MeV/c²
Electron charge-to-mass ratio
\(\frac{e}{m_e} = 1.758\,820 \times 10^{11}\) C/kg
Rydberg constant
\(R_\infty = 10\,973\,731.568\,160\) m⁻¹
Fine-structure constant
\(\alpha = \frac{e^2}{4\pi\varepsilon_0\hbar c} \approx \frac{1}{137.036}\)
Hartree energy
\(E_h = 4.359\,744\,72 \times 10^{-18}\) J
≈ 27.211 eV
Bohr radius
\(a_0 = 5.291\,772\,109 \times 10^{-11}\) m
≈ 0.529 Å
💎Semiconductor Constants
Silicon (Si)
Silicon lattice constant
\(a_{\text{Si}} = 543.102\) pm
at 300 K
Silicon bandgap
\(E_g = 1.12\) eV
at 300 K
Intrinsic carrier concentration (Si)
\(n_i \approx 1.5 \times 10^{10}\) cm⁻³
at 300 K
Silicon relative permittivity
\(\varepsilon_r = 11.7\)
Electron mobility (Si)
\(\mu_n \approx 1400\) cm²/(V·s)
at 300 K
Hole mobility (Si)
\(\mu_p \approx 450\) cm²/(V·s)
at 300 K
Other Semiconductors
| Material | Bandgap (eV) | Electron Mobility (cm²/V·s) | Relative Permittivity |
|---|---|---|---|
| Germanium (Ge) | 0.66 | 3900 | 16.0 |
| Gallium Arsenide (GaAs) | 1.42 | 8500 | 12.9 |
| Gallium Nitride (GaN) | 3.4 | 1000 | 9.0 |
| Silicon Carbide (SiC) | 3.26 | 900 | 9.7 |
| Indium Phosphide (InP) | 1.35 | 5400 | 12.5 |
Thermal voltage
\(V_T = \frac{k_B T}{e} \approx 25.85\) mV
at 300 K (≈ 27°C)
Thermal energy
\(k_B T \approx 26\) meV
at 300 K
🔌Circuit & Component Constants
Standard Component Values
E-Series Standard Resistor Values
E12 Series (10% tolerance): 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
E24 Series (5% tolerance): 10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91
Conductor Resistivity (at 20°C)
| Material | Resistivity (Ω·m) | Conductivity (S/m) | Temp. Coeff. (1/K) |
|---|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 6.30 × 10⁷ | 0.0038 |
| Copper | 1.68 × 10⁻⁸ | 5.96 × 10⁷ | 0.00386 |
| Gold | 2.44 × 10⁻⁸ | 4.10 × 10⁷ | 0.0034 |
| Aluminum | 2.65 × 10⁻⁸ | 3.77 × 10⁷ | 0.0039 |
| Tungsten | 5.60 × 10⁻⁸ | 1.79 × 10⁷ | 0.0045 |
Standard wire gauge (AWG)
AWG 0: 8.25 mm diameter
Each 6 AWG decrease doubles area
PCB copper thickness (1 oz)
35 μm (1.4 mil)
Standard PCB copper
Dielectric Constants
| Material | Relative Permittivity (εᵣ) | Application |
|---|---|---|
| Air | 1.00059 | Reference |
| Teflon (PTFE) | 2.1 | High-freq cables |
| Polyethylene | 2.25 | Coaxial cables |