1Fundamental Quantities
Current
I = Q / tI equals Q divided by t.
Q = I × tQ equals I times t.
I=current (A) · Q=charge (C) · t=time (s) · 1 A = 1 C/s
Voltage
V = E / QV equals E divided by Q.
E = V × QE equals V times Q.
V=volts · E=energy (J) · Q=coulombs · 1 V = 1 J/C
Voltage = energy per coulomb across a load. Loads transfer energy, not charge.
Power & Energy
P = E / tP equals E divided by t.
E = P × tE equals P times t.
1 W = 1 J/s
P = V × IP equals V times I.
I = P/V · V = P/IRearranged forms of P = V × I.
2Ohm's Law
V = I × RV equals I times R.
I = V / RI equals V divided by R.
R = V / IR equals V divided by I.
V=volts · I=amperes · R=ohms (Ω)
3Resistive Power / Heating
P = I² × RP equals I squared times R.
P = V² / RP equals V squared divided by R.
Also P = V × I — see §1.
Cable heating rises with the square of current.
4Series Circuits
Resistance
Rtotal = R1+R2+R3+…Total R equals R one plus R two, and so on.
Voltage
Vtotal = V1+V2+V3+…Total V equals V one plus V two, and so on.
Current
I1 = I2 = I3 = ItotalCurrent is the same through every series component.
Voltage divider
Vx = Vs × (Rx/Rtotal)V x equals supply V times R x over total R.
Series: same current, voltage divides.
5Parallel Circuits
Voltage
V1 = V2 = V3 = VsupplyEach branch voltage equals the supply voltage.
Current — KCL
Itotal = I1+I2+I3+…Total current equals the sum of branch currents.
Resistance
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.
Parallel: same voltage, current divides.
6Kirchhoff's Laws
Current law — KCL
Σ Iin = Σ IoutSum of currents in equals sum of currents out.
Voltage law — KVL
Σ V = 0Sum of voltages round a closed loop is zero.
Vsupply = Vdrop1+Vdrop2+…Practical form of KVL.
7Cable Resistance
R = ρ × L / AR equals rho times L divided by A.
R=resistance · ρ (rho)=resistivity · L=length · A=cross-sec. area
Rloop = 2 × ρ × L / ALoop R equals two times rho times L over A.
Use factor 2 only when L is the one-way length.
Longer cable → more R. Larger area → less R.
8Voltage Drop & Cable Loss
ΔV = I × RVoltage drop equals current times resistance.
VD% = (ΔV/Vsupply) × 100VD % equals ΔV over supply V, times 100.
ΔV = (mV/A/m × I × L)/1000mV per A per m, times I, times L, over 1000.
mV/A/m value must come from the applicable cable/design tables.
Ploss = I² × RPower loss equals current squared times R.
9Energy / Billing
Energy (kWh) = P (kW) × t (h)Energy equals power times time.
Cost = kWh × tariffCost equals kilowatt-hours times tariff.
1000 W = 1 kW · 1000 Wh = 1 kWh
10Efficiency
η = Pout / PinEta equals output power over input power.
η% = (Pout/Pin) × 100Efficiency % equals that ratio times 100.
η (eta) = efficiency
11AC Fundamentals
f = 1/T · T = 1/fFrequency and period are reciprocals.
f=frequency (Hz) · T=period (s)
50 Hz → T = 0.02 s = 20 ms
ω = 2πfOmega equals two pi times frequency.
ω (omega) = angular frequency
v(t) = Vpeak × sin(2πft)Instantaneous voltage — sine-wave reference.
12RMS & Peak AC Values
Vrms = Vpeak / √2RMS V equals peak V over root two.
Vpeak = Vrms × √2Peak V equals RMS V times root two.
Irms = Ipeak / √2 · Ipeak = Irms × √2Same relationship for current.
230 V RMS ≈ 325 V peak
13Capacitors
Q = C × VCharge equals capacitance times voltage.
C=capacitance (F)
E = ½ C V²Energy equals half C times V squared.
XC = 1 / (2πfC)X C equals one over two pi f C.
Higher frequency → lower capacitive reactance.
14Inductors
V = L × (ΔI/Δt)Voltage equals L times change in I over change in t.
E = ½ L I²Energy equals half L times I squared.
XL = 2πfLX L equals two pi f L.
Higher frequency → higher inductive reactance.
15Impedance
Z = V/I · I = V/ZImpedance equals voltage over current.
Z = √(R² + (XL−XC)²)Series R-L-C impedance.
Z=ohms · R=resistance · XL=inductive react. · XC=capacitive react.
16AC Power
S = V × IApparent power (VA).
P = V × I × cos φReal power (W).
Qreactive = V × I × sin φReactive power (var).
S² = P² + Q²Power triangle.
PF = cos φ = P/SPower factor.
φ (phi) = phase angle between V and I
Purely resistive load: PF ≈ 1, so P ≈ V × I.
17Transformers
Vp/Vs = Np/NsVoltage ratio equals turns ratio.
Ip/Is = Ns/NpCurrent ratio is the inverse turns ratio.
Vp × Ip ≈ Vs × IsIdeal power in ≈ power out.
p=primary · s=secondary · N=number of turns
18Single-Phase Power
P = V × IResistive load.
P = V × I × PFGeneral AC load.
19Three-Phase Power
P = √3 × VL × IL × cos φReal power, balanced 3-phase.
S = √3 × VL × ILApparent power.
Q = √3 × VL × IL × sin φReactive power.
VL=line-to-line V · IL=line current
EU 230/400 V system: Line–Neutral ≈ 230 V · Line–Line ≈ 400 V
20Star & Delta
Star / Wye
VL = √3 × Vphase · IL = IphaseLine V is √3 × phase V; line I = phase I.
Delta
VL = Vphase · IL = √3 × IphaseLine V = phase V; line I is √3 × phase I.
21RCD / Residual Current
IΔ = |IL − IN|Residual current = |Live I − Neutral I|.
IΔ=residual/differential current
e.g. 5.000 A − 4.975 A = 0.025 A = 25 mA
MCB → excess current. RCD → current imbalance.
22Fault Current / Earth-Fault Loop
Ifault = U0 / ZsFault current equals U zero over Zs.
Zs = Ze + (R1+R2)Zs equals Ze plus R one plus R two.
Zs ≤ U0 / IaZs must not exceed U zero over Ia.
U0=nom. V to earth · Ze=external loop Z · R1=line R · R2=CPC R · Ia=device trip current
Actual permitted Zs & disconnection times: use applicable regs/device tables.
23Basic Circuit Design Relationship
Ib ≤ In ≤ Iz
I b is less than or equal to I n, less than or equal to I z.
Ib=design/load current · In=device rating · Iz=cable capacity — load → protective device → cable
24Protective Conductor (Adiabatic)
ADVANCED
S = √(I²t) / kS equals root of I-squared-t, over k.
S = I√t / kEquivalent form.
S=required c.s.a. · I=fault current · t=disconnection time · k=material/insulation constant. Use with applicable regs/tables.
25Motor Basics
ns = 120f / pSync. speed = 120 × f, over pole count.
ns=sync. speed (rpm) · p=number of poles
Slip% = ((ns−nr)/ns) × 100Slip % = (sync − rotor speed)/sync, ×100.
nr=actual rotor speed
Pmech = τ × ωMechanical power = torque × angular velocity.
τ (tau) = torque (N·m) · ω (omega) = ang. velocity (rad/s)
26Prefixes & Conversions
1 kA = 1000 A · 1 A = 1000 mA · 1 mA = 0.001 A
1 kV = 1000 V · 1 kW = 1000 W · 1 kΩ = 1000 Ω
1 MΩ = 1,000,000 Ω · 1 mF = 10⁻³ F · 1 µF = 10⁻⁶ F · 1 nF = 10⁻⁹ F
√2 ≈ 1.414 · √3 ≈ 1.732 · π ≈ 3.142
Mental Model — hold onto these
Current: charge per second.
Voltage: potential-energy diff. per coulomb.
Resistance: opposition to current.
Power: rate of energy transfer.
Load: transfers energy, not charge.
Series: same current, V divides.
Parallel: same voltage, I divides.
MCB: protects against overcurrent.
RCD: detects L–N current imbalance.
PE: protective fault-current path.
Neutral: near earth potential, not "used-up Live".
Ib≤In≤Iz: load → device → cable.