Formulas

I = Q / t

“I equals Q divided by t.”

I current (A) · Q charge (C) · t time (s) · 1 A = 1 C/s

Q = I × t

“Q equals I times t.”

V = E / Q

“V equals E divided by Q.”

1 V = 1 J/C

Loads transfer energy; they do not consume charge.

E = V × Q

“E equals V times Q.”

P = E / t

“P equals E divided by t.”

1 W = 1 J/s

E = P × t

“E equals P times t.”

P = V × I

“P equals V times I.”

I = P / V

“I equals P divided by V.”

V = P / I

“V equals P divided by I.”

V = I × R

“V equals I times R.”

I = V / R

“I equals V divided by R.”

R = V / I

“R equals V divided by I.”

P = I² × R

“P equals I squared times R.”

Cable heating rises with the square of current.

P = V² / R

“P equals V squared divided by R.”

Rtotal = R1 + R2 + R3 + …

“Total resistance equals R one plus R two, and so on.”

Series: same current, voltage divides.

Vtotal = V1 + V2 + V3 + …

“Total voltage equals V one plus V two, and so on.”

I1 = I2 = I3 = Itotal

“Current is the same through every series component.”

Vx = Vs × (Rx / Rtotal)

“V x equals supply V times R x over total R.”

V1 = V2 = V3 = Vsupply

“Each branch voltage equals the supply voltage.”

Parallel: same voltage, current divides.

Itotal = I1 + I2 + I3 + …

“Total current equals the sum of branch currents.”

1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …

“Reciprocal of total R equals sum of reciprocals.”

Rtotal = (R1 × R2) / (R1 + R2)

“Two resistors: product over sum.”

Σ Iin = Σ Iout

“Sum of currents in equals sum of currents out.”

Σ V = 0

“Sum of voltages around a closed loop is zero.”

Vsupply = Vdrop1 + Vdrop2 + …

Practical form of KVL.

R = ρ × L / A

“R equals rho times L divided by A.”

ρ (rho) = resistivity · L = length · A = area

Longer cable → more R. Larger area → less R.

Rloop = 2 × ρ × L / A

“Loop R equals two times rho times L over A.”

Use 2 only when L is the one-way length.

ΔV = I × R

“Voltage drop equals current times resistance.”

VD% = (ΔV / Vsupply) × 100

“Drop % equals ΔV over supply V, times 100.”

ΔV = (mV/A/m × I × L) / 1000

“mV per A per m, times I, times L, over 1000.”

Use the table mV/A/m for the cable.

Ploss = I² × R

“Power loss equals I squared times cable R.”

Energy (kWh) = P (kW) × t (h)

“Energy equals power times time.”

1000 W = 1 kW · 1000 Wh = 1 kWh

Cost = kWh × tariff

“Cost equals kilowatt-hours times tariff.”

η = Pout / Pin

“Eta equals output power over input power.”

η% = (Pout / Pin) × 100

“Efficiency % equals that ratio times 100.”

f = 1 / T

“Frequency equals one divided by period.”

50 Hz → T = 0.02 s = 20 ms

T = 1 / f

“Period equals one divided by frequency.”

ω = 2πf

“Omega equals two pi times frequency.”

v(t) = Vpeak × sin(2πft)

Instantaneous sine-wave voltage.

Vrms = Vpeak / √2

“RMS V equals peak V over root two.”

230 V RMS ≈ 325 V peak

Vpeak = Vrms × √2

“Peak V equals RMS V times root two.”

Irms = Ipeak / √2   ·   Ipeak = Irms × √2

Same RMS/peak relationship for current.

Q = C × V

“Charge equals capacitance times voltage.”

E = ½ C V²

“Energy equals half C times V squared.”

XC = 1 / (2πfC)

“X C equals one over two pi f C.”

Higher frequency → lower XC.

V = L × (ΔI / Δt)

“Voltage equals L times change in I over change in t.”

E = ½ L I²

“Energy equals half L times I squared.”

XL = 2πfL

“X L equals two pi f L.”

Higher frequency → higher XL.

Z = V / I   ·   I = V / Z

“Impedance equals voltage over current.”

Z = √(R² + (XL − XC)²)

Series R-L-C impedance.

S = V × I

Apparent power (VA).

P = V × I × cos φ

Real power (W).

Qreactive = V × I × sin φ

Reactive power (var).

S² = P² + Q²

Power triangle.

PF = cos φ = P / S

Power factor equals real power over apparent power.

Resistive load: PF ≈ 1, so P ≈ V × I.

Vp / Vs = Np / Ns

Voltage ratio equals turns ratio.

Ip / Is = Ns / Np

Current ratio is the inverse turns ratio.

Vp × Ip ≈ Vs × Is

Ideal: power in ≈ power out.

P = V × I × PF

Single-phase AC power.

P = √3 × VL × IL × cos φ

Balanced three-phase real power.

EU: Line–Neutral ≈ 230 V · Line–Line ≈ 400 V

S = √3 × VL × IL

Three-phase apparent power.

Q = √3 × VL × IL × sin φ

Three-phase reactive power.

Star: VL = √3 × Vphase   ·   IL = Iphase

Star: line V is √3 × phase V; line I = phase I.

Delta: VL = Vphase   ·   IL = √3 × Iphase

Delta: line V = phase V; line I is √3 × phase I.

IΔ = |IL − IN|

Residual current = |Live I − Neutral I|.

MCB → excess current. RCD → imbalance.

Ifault = U0 / Zs

Fault current equals U zero over Zs.

Zs = Ze + (R1 + R2)

Zs equals Ze plus R one plus R two.

Zs ≤ U0 / Ia

Zs must not exceed U zero over Ia.

Use the applicable regs/device tables.

Ib ≤ In ≤ Iz

Load current ≤ device rating ≤ cable capacity.

load → protective device → cable

S = √(I²t) / k

Required CPC area. Advanced — use regs/tables.

S = I√t / k

Equivalent form of the adiabatic equation.

ns = 120f / p

Synchronous speed = 120 × f, over pole count.

Slip% = ((ns − nr) / ns) × 100

Slip % = (sync − rotor) / sync, × 100.

Pmech = τ × ω

Mechanical power = torque × angular velocity.

τ (tau) = N·m · ω (omega) = rad/s

Prefixes

1 kA = 1000 A · 1 A = 1000 mA · 1 kV = 1000 V · 1 kW = 1000 W
1 kΩ = 1000 Ω · 1 MΩ = 1,000,000 Ω · √2 ≈ 1.414 · √3 ≈ 1.732 · π ≈ 3.142