DC Fundamentals
Ohm's Law
V = I × R
Voltage = Current × Resistance
Power (V×I)
P = V × I
Power = Voltage × Current
Power (I²R)
P = I² × R
Power = Current² × Resistance
Power (V²/R)
P = V² / R
Power = Voltage² / Resistance
Energy
E = P × t
Energy = Power × Time (joules)
Charge
Q = I × t
Charge = Current × Time (coulombs)
Resistor Networks
Series Resistance
Rₜ = R₁ + R₂ + … + Rₙ
Total = sum of all resistors
Parallel Resistance (2)
Rₜ = (R₁ × R₂) / (R₁ + R₂)
Product over sum for 2 resistors
Parallel Resistance (N)
1/Rₜ = 1/R₁ + 1/R₂ + … + 1/Rₙ
Reciprocal sum for N resistors
Voltage Divider
Vₒᵤₜ = Vᵢₙ × R₂ / (R₁ + R₂)
Output voltage from two series resistors
Current Divider
I₁ = Iₜ × R₂ / (R₁ + R₂)
Current through R₁ in a 2-branch parallel
Capacitors & Inductors
Capacitance
C = Q / V
Capacitance = Charge / Voltage
Series Capacitance
1/Cₜ = 1/C₁ + 1/C₂ + …
Reciprocal sum (opposite of resistors)
Parallel Capacitance
Cₜ = C₁ + C₂ + …
Direct sum
RC Time Constant
τ = R × C
Time to reach 63.2% charge
Capacitor Energy
E = ½CV²
Energy stored in a capacitor
Inductor Energy
E = ½LI²
Energy stored in an inductor
RL Time Constant
τ = L / R
Inductor time constant
AC Circuits
Capacitive Reactance
Xc = 1 / (2πfC)
Opposition to AC by a capacitor
Inductive Reactance
XL = 2πfL
Opposition to AC by an inductor
Impedance (RLC)
Z = √(R² + (XL − Xc)²)
Total impedance of series RLC
Resonant Frequency
f₀ = 1 / (2π√(LC))
Frequency where XL = Xc
RMS Voltage
Vrms = Vpeak / √2
Root Mean Square of sinusoidal voltage
Semiconductors
LED Resistor
R = (Vs − Vf) / If
Current limiting resistor for LED
Transistor β
β = Ic / Ib
DC current gain (hFE)
Collector Current
Ic = β × Ib
From base current × gain