Basic Physical Quantities and Laws

Charge and Electric Field

Charge

Symbol: Q
Unit: Coulomb (C)
Definition: A fundamental property of matter, existing in positive and negative forms
Charge of 1 electron: e = 1.602 × 10⁻¹⁹ C
1 C = 6.24 × 10¹⁸ electron charges

Like charges repel, opposite charges attract

Electric Field

Symbol: E
Unit: V/m (Volts per meter)
Definition: The force experienced by a unit positive charge
Formula: E = F / q
      F = k × Q₁Q₂ / r²  (Coulomb's Law, k = 9×10⁹ N·m²/C²)

Three Fundamental Quantities

Voltage

Symbol: V or U
Unit: Volt (V)
Definition: The potential difference between two points, the "pressure" driving charge flow
Analogy: Water pressure — the greater the water level difference, the stronger the flow

1 V = 1 J/C  (Doing 1 Joule of work to move 1 Coulomb of charge)

Current

Symbol: I
Unit: Ampere (A)
Definition: The amount of charge passing through a conductor's cross-section per unit time
Formula: I = ΔQ / Δt
Analogy: Water flow — the volume of water flowing through a pipe per unit time

Direction: Direction of positive charge flow (actual electron flow is in the opposite direction)

Resistance

Symbol: R
Unit: Ohm (Ω)
Definition: The property that opposes the flow of current

Determining factors: R = ρ × L / A
  ρ: Resistivity (Ω·m)
  L: Length (m)
  A: Cross-sectional area (m²)

Analogy: Pipe thickness and length — the thinner and longer the pipe, the greater the resistance

Conductance

Symbol: G
Unit: Siemens (S)
Formula: G = 1 / R

Core Laws

Ohm's Law

V = I × R
I = V / R
R = V / I

If any two are known, the third can be calculated.
Applies to linear resistors; not applicable to semiconductor devices!

Power

P = V × I          (General)
P = I² × R         (Resistive heating — Joule's Law)
P = V² / R

Unit: Watt (W)
Energy: W = P × t  (Joule J, electricity bills are in kWh)

Kirchhoff's Laws

KCL — Current Law (Node)

KVL — Voltage Law (Loop)

In a closed loop, the algebraic sum of voltages across each segment is zero

    ┌── R1 ──┬── R2 ──┐
    │   +V1 -│  +V2 - │
    │        │        │
    └── Vs ──┴────────┘

Vs - V1 - V2 = 0
i.e., ΣV = 0 (around the entire loop)

Essence: Conservation of energy (the electric field is a conservative field)

Application Example

         R1=2Ω    R2=3Ω
    ┌────┤├───────┤├────┐
    │                    │
   ─┼─  Vs=10V          R3=5Ω
   ─┼─                   │
    │                    │
    └────────────────────┘

KCL (Node A): I1 = I2 + I3
KVL (Loop 1, Left): 10 - 2I1 - 5I3 = 0
KVL (Loop 2, Right): 5I3 - 3I2 = 0

Solving the simultaneous equations → I1=2A, I2=1.25A, I3=0.75A

Basic Circuit Structures

Series

  R1=2Ω    R2=3Ω    R3=5Ω
──┤├──────┤├──────┤├──

Equivalent Resistance: Rt = R1 + R2 + R3 = 10Ω
Current: Same everywhere It = I1 = I2 = I3
Voltage: Vt = V1 + V2 + V3 (Voltage division)

Parallel

──┬──┤├──┬──
  │  R1  │
  ├──┤├──┤
  │  R2  │
──┴──┤├──┴──

Equivalent Resistance: 1/Rt = 1/R1 + 1/R2
          Rt = (R1×R2)/(R1+R2)  (for two resistors)

Current: It = I1 + I2 (Current division)
Voltage: Same everywhere Vt = V1 = V2

Series-Parallel (Mixed)

Simplify the parallel parts first → then treat as series
Simplify step-by-step from inside out

Common Prefixes

Common Signal Waveforms

AC Parameters

Peak Value Vp: Maximum value
Peak-to-Peak Vpp: Distance between positive and negative peaks = 2×Vp
RMS Value Vrms: For sine wave = Vp/√2 ≈ 0.707Vp
            (Equivalent DC value for thermal effects)

Frequency f: Number of cycles per second (Hz)
Period T: T = 1/f
Angular Frequency ω: ω = 2πf

Keywords: Voltage, Current, Resistance, Ohm's Law, KVL, KCL, Power, Series, Parallel, AC, RMS