Electrical Formula Reference

Complete guide for Period 1 & 2 Apprenticeship Studies

AC Fundamentals

Frequency from Speed
f = p × n / 120
f: frequency (Hz), p: poles, n: RPM
Period
T = 1 / f
Period in seconds
Angular Velocity
ω = 2πf
Radians per second
Instantaneous Voltage
v = Vp × sin(ωt)
Vp: peak voltage
RMS Voltage
Vrms = 0.707 × Vp
Also: Vrms = Vp / √2
Peak from RMS
Vp = 1.414 × Vrms
Also: Vp = Vrms × √2
Average Voltage
Vavg = 0.637 × Vp
Over half-cycle
Peak-to-Peak
Vpp = 2 × Vp
Peak to peak voltage

Ohm's Law & Power

Voltage
V = IR
Volts, Amps, Ohms
Current
I = V / R
Current in amperes
Resistance
R = V / I
Resistance in ohms
Power (VI)
P = VI
Watts
Power (I²R)
P = I²R
Power dissipated in resistor
Power (V²/R)
P = V² / R
Alternative power formula

Inductors

Inductive Reactance
XL = 2πfL
L: inductance (H), f: frequency (Hz)
Time Constant
τ = L / R
Tau in seconds
Stored Energy
E = ½LI²
Joules
Induced Voltage
VL = L × (di/dt)
Rate of current change

Capacitors

Capacitive Reactance
XC = 1 / (2πfC)
C: capacitance (F), f: frequency (Hz)
Time Constant
τ = RC
Tau in seconds
Stored Energy
E = ½CV²
Joules
Displacement Current
IC = C × (dv/dt)
Rate of voltage change

Impedance

Impedance Magnitude
Z = √(R² + X²)
X = XL - XC (net reactance)
Phase Angle
θ = arctan(X / R)
Degrees or radians
Power Factor
PF = cos(θ) = R / Z
0 to 1 (ideal = 1.0)

Power Triangle

Apparent Power
S = VI (VA)
Volt-Amperes
Real Power
P = VI × cos(θ) (W)
Watts, actual work done
Reactive Power
Q = VI × sin(θ) (VAR)
Volt-Amperes Reactive
Pythagorean Relationship
S = √(P² + Q²)
Apparent power formula

Transformers

Voltage Ratio
V1 / V2 = N1 / N2
Primary to secondary turns
Current Ratio
I1 / I2 = N2 / N1
Inverse of turns ratio
Power Rating
kVA = V × I / 1000
Kilovolt-Amperes

CEC Calculations

Voltage Drop
VD = 2 × I × R × L / 1000
Max 3% branch, 5% total (CEC)
Fault Current
I_fault = (kVA × 1000) / (V × %Z)
Short circuit current calculation
Conduit Fill
Fill % ≤ 40%
3+ conductors or cables per CEC Rule 12-614

Time Constants (RC/RL)

Full Charge/Discharge
t = 5τ (99.3%)
Practical fully charged/discharged
At 1 Time Constant
t = 1τ (63.2%)
One tau
At 2 Time Constants
t = 2τ (86.5%)
Two tau
At 3 Time Constants
t = 3τ (95%)
Three tau

Motor Control

Stop Circuits
Connected in SERIES
Safety critical: Any stop must break circuit
Start Circuits
Connected in PARALLEL
Any start pushes can activate contactor
Seal-in Voltage
≈ 85% of rated voltage
Holds contactor after start button release
Drop-out Voltage
≈ 50% of rated voltage
Contactor releases below this voltage