Ohm's Law & DC Circuits
Enter exactly 2 of V, I, R, P — all 6 pairs solved. Entering 3+ values triggers overdetermined consistency check (2% tolerance).
⚡Known Values — Enter Any Two
📊Results
Voltage V
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Current I
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Resistance R
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Power P
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Energy (1 hr)
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Conductance G
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Series R_eq
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Parallel R_eq
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V = I×R | P = V×I = I²×R = V²/R
G = 1/R | R_s = ΣRᵢ | 1/R_p = Σ(1/Rᵢ)
G = 1/R | R_s = ΣRᵢ | 1/R_p = Σ(1/Rᵢ)
AC Power Analysis
Single / three-phase apparent, active, reactive power + energy cost + PFC
🔋AC Power Inputs
📊Power Results
Apparent Power S
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Active Power P (electrical)
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Reactive Power Q
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Phase Angle φ
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Phase Voltage Vφ (line-to-neutral)
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Input Power (incl. η)
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η Semantics Note
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PFC Capacitor (to PF=0.95)
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Annual Energy
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Annual Cost
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1φ: S=Vφ×I | 3φ: S=√3×VL×IL | Vφ=VL/√3 (3φ)
P=S·cosφ | Q=S·sinφ (real only if PF∈(0,1]) | Qc = P×(tanφ₁ − tanφ₂)
η(motor)=P_shaft/P_elec | η(heater)=P_useful/P_input
P=S·cosφ | Q=S·sinφ (real only if PF∈(0,1]) | Qc = P×(tanφ₁ − tanφ₂)
η(motor)=P_shaft/P_elec | η(heater)=P_useful/P_input
Cable / Conductor Sizing
Current rating, voltage drop & minimum cross-section (IEC 60364 / NEC)
🔌Cable Inputs
⚡ Derating Factors (IEC 60364-5-52 / IEC 60287)
ℹLV trefoil: X ≈ 0.08 mΩ/m — suitable for LV design.
📊Cable Results
Cable R (temp-corrected)
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Reactance X (est.)
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Voltage Drop ΔV
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VD Status
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Min CSA for VD Limit
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Cable Power Loss
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Current Density
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Resistance / km
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Derated Ampacity Check (k_T × k_G × k_i × I_table)
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Enter tabulated I_z below or check IEC 60364-5-52. Load current must not exceed derated ampacity.
Combined Derating Factor (k_T × k_G × k_i)
—
R = ρ(T)×L/A (per cond.) | 1φ: ΔV=2I(Rcosφ+Xsinφ)
3φ: ΔV=√3·I·(Rcosφ+Xsinφ) | 1φ: A_min=2ρLIcosφ/ΔV_max | 3φ: A_min=√3·ρ·L·I·cosφ/ΔV_max
R_T = R₂₀[1 + α(T−20)] | αCu=0.00393 | αAl=0.00403
Iz_derated = Iz_table × k_T × k_G × k_i (IEC 60364-5-52) | I_design ≤ Iz_derated
3φ: ΔV=√3·I·(Rcosφ+Xsinφ) | 1φ: A_min=2ρLIcosφ/ΔV_max | 3φ: A_min=√3·ρ·L·I·cosφ/ΔV_max
R_T = R₂₀[1 + α(T−20)] | αCu=0.00393 | αAl=0.00403
Iz_derated = Iz_table × k_T × k_G × k_i (IEC 60364-5-52) | I_design ≤ Iz_derated
Voltage Drop & Protection
VD analysis with MCB/fuse sizing to NEC 430 / IEC standards
📉Circuit Parameters
📊Voltage Drop Results
Voltage Drop ΔV
—
—
Receiving End Voltage
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VD Status
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Cable Resistance
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Power Loss
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Recommended Breaker / Fuse
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Min Cable for 5% VD
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Current Density
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1φ: ΔV = 2·I·(R·cosφ + X·sinφ) | 3φ: ΔV = √3·I·(R·cosφ + X·sinφ)
R=ρ(T)·L/A per cond. | X≈0.08 mΩ/m | Breaker: 125% motor, 115% other
R=ρ(T)·L/A per cond. | X≈0.08 mΩ/m | Breaker: 125% motor, 115% other
Electric Motor Calculator
3-phase induction motor — FLC, torque, slip, starting current (DOL / Y-Δ / VFD)
⚙️Motor Parameters
📊Motor Results
Full-Load Current IL
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SF-Adjusted Current (IL × SF)
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Input Power
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Apparent Power S
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Rated Torque
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Synchronous Speed Ns
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Slip %
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Starting Current (selected method)
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Starting Torque
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Reactive Power Q
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Recommended Breaker (NEC 430 / IEC)
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IL = P_shaft/(√3·V·η·cosφ) | T = P_shaft_W/(2π·n/60)
P_shaft [W] = kW_rated × 1000 | Pin = P_shaft / η | T uses SHAFT watts, not Pin — prevents torque overestimate
Ns = 60f/p | s = (Ns−N)/Ns | Y-Δ: Is = DOL/3 (load torque must be <33% rated at switchover)
BUG4 fix: IL_SF = IL × SF — cable and protection must be rated for SF-adjusted current (IEC/NEMA)
BUG5 note: Istart multiplier per IEC 60034 LRC — actual value depends on rotor design & supply Z
BUG6 note: Y-Δ formula Is=DOL/3 valid only if motor RUNS in delta — verify motor winding connection
P_shaft [W] = kW_rated × 1000 | Pin = P_shaft / η | T uses SHAFT watts, not Pin — prevents torque overestimate
Ns = 60f/p | s = (Ns−N)/Ns | Y-Δ: Is = DOL/3 (load torque must be <33% rated at switchover)
BUG4 fix: IL_SF = IL × SF — cable and protection must be rated for SF-adjusted current (IEC/NEMA)
BUG5 note: Istart multiplier per IEC 60034 LRC — actual value depends on rotor design & supply Z
BUG6 note: Y-Δ formula Is=DOL/3 valid only if motor RUNS in delta — verify motor winding connection
Transformer Calculator
Turns ratio, efficiency, voltage regulation, short-circuit current
🔁Transformer Parameters
📊Transformer Results
Turns Ratio N1/N2
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%Reactance X%
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Primary FLC I1
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Secondary FLC I2
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Efficiency at Load
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Voltage Regulation
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Max Efficiency at
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Short-Circuit Current (HV side)
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a = V1/V2 | η = x·kVA·1000·cosφ / (x·kVA·1000·cosφ + Pfe + x²·Pcu) [all in W]
VR(lag) = R%·cosφ + X%·sinφ | VR(lead) = R%·cosφ − X%·sinφ (Kapp approx., valid to ~full-load)
x_maxη = √(Pfe/Pcu) | I_sc = I₁_FLC / (Z%/100)
VR(lag) = R%·cosφ + X%·sinφ | VR(lead) = R%·cosφ − X%·sinφ (Kapp approx., valid to ~full-load)
x_maxη = √(Pfe/Pcu) | I_sc = I₁_FLC / (Z%/100)
Capacitor & RC/LC Circuits
Capacitor energy, RC time constant, resonance, Q-factor, impedance
🔆Component Values
📊Circuit Results
Capacitive Reactance Xc
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Inductive Reactance XL
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Energy Stored E
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Charge Q = C×V
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Resonant Freq f₀
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Angular ω₀ (rad/s)
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RC Time Constant τ
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Q-Factor
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Impedance |Z| at f
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Capacitor Current Ic
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C[F]=C_µF×10⁻⁶ | L[H]=L_mH×10⁻³ (unit conversion — prevents 1000× error)
Xc = 1/(2πfC[F]) | XL = 2πfL[H] | f₀ = 1/(2π√(L[H]·C[F])) [Hz, always correct]
Series RLC: Q = (1/R)·√(L/C) | Parallel RLC: Q = R/√(L/C) | τ=RC | E=½CV²
Xc = 1/(2πfC[F]) | XL = 2πfL[H] | f₀ = 1/(2π√(L[H]·C[F])) [Hz, always correct]
Series RLC: Q = (1/R)·√(L/C) | Parallel RLC: Q = R/√(L/C) | τ=RC | E=½CV²
Short Circuit / Fault Analysis
3-phase & 1-phase fault currents, fault MVA, breaker kA rating (IEC 60909)
💥System Parameters
🔌 Grid / Source
🔁 Transformer
⚙️ Motor Contribution (optional)
🔌 Cable to Fault Point
📊Fault Results
3-Phase Isc3 (symmetrical rms)
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Peak Asymmetrical Current Ip
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IEC 60909 κ factor
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Motor Contribution
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Total Isc (incl. motors)
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Phase-Phase Isc2
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1-Phase Isc1 (approx.)
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Fault MVA (3-phase)
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Grid Source Z (X/R=10)
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Transformer Z (R+jX)
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Cable Z (R + jX components)
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Total Z_total (magnitude + X/R)
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Minimum Breaker kA Rating (based on Ip)
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IEC 60909: Isc3 = c·Vn/(√3·|Z_total|) | c=1.05 (LV max fault)
Ip = κ·√2·Isc3 | κ = 1.02 + 0.98·e^(−3/XR) | Z_cable = R+jX (R=ρL/A, X≈0.08mΩ/m)
Motor contrib: I_mot ≈ 6×FLC | Breaker rated on Ip (peak)
⚠ BUG8: This uses simplified impedance network (no full per-unit system). For accurate fault studies use IEC 60909 software with complete network model. Error may exceed ±50% on complex networks.
Ip = κ·√2·Isc3 | κ = 1.02 + 0.98·e^(−3/XR) | Z_cable = R+jX (R=ρL/A, X≈0.08mΩ/m)
Motor contrib: I_mot ≈ 6×FLC | Breaker rated on Ip (peak)
⚠ BUG8: This uses simplified impedance network (no full per-unit system). For accurate fault studies use IEC 60909 software with complete network model. Error may exceed ±50% on complex networks.
Illumination Design
Lumen method — luminaire count, lux levels, layout, watt density (IS 3646 / IES)
💡Room & Luminaire Data
🏠 Room Dimensions
🏢 Occupancy
💡 Luminaire
📊Illumination Results
Luminaires Required N
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Achieved Illuminance
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Room Index RI (k)
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Total Installed Load
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Watt Density (W/m²)
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Floor Area
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Luminaire Layout
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Spacing S_Length
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Spacing S_Width
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N = E×A / (F×MF×UF) | RI = L×W/(Hm×(L+W))
IS 3646: Office ≥500 lux | Lab ≥750 lux | Watt density = W_total/A
IS 3646: Office ≥500 lux | Lab ≥750 lux | Watt density = W_total/A
HV Cable Test
Recommended hi-pot withstand test voltage & duration per IEC 60502, IEC 60840, IEEE Std 400, IS 7098. Insulation resistance limits included.
🔬Cable & Test Parameters
Cable System
Test Setup
📊Test Recommendations
Recommended Test Voltage
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Test Duration
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Test Standard
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Pass Criterion
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Sheath Test
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Min IR (at 20°C)
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IR Temperature Note
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⚠
High voltage testing is life-threatening. Authorised personnel only. Maintain exclusion zone, earth all conductors, use rated test leads. Discharge cable after every test.
IEC 60502-4 site (XLPE): U_test = 2×Uo, 60 min
IEEE 400.2 VLF: 1.73–2×Uo, 60 min (preferred for XLPE)
DC (legacy): 3–4×Uo, 15 min | IR_min ≈ (Uo+1) MΩ/km
IEEE 400.2 VLF: 1.73–2×Uo, 60 min (preferred for XLPE)
DC (legacy): 3–4×Uo, 15 min | IR_min ≈ (Uo+1) MΩ/km
Education Hub
Core theory, formulas, reference tables & self-test quiz — for students and working engineers
⚡Ohm's Law & DC Circuits
Ohm's Law
The fundamental relationship between voltage (V), current (I) and resistance (R). Valid for linear (ohmic) conductors at constant temperature. Discovered by Georg Simon Ohm in 1827.
V = I × R | P = V×I = I²×R = V²/R
I = V/R | R = V/I | Energy E = P×t (Joules)
I = V/R | R = V/I | Energy E = P×t (Joules)
Series & Parallel Resistors
Series: same current through all, voltage divides. Parallel: same voltage across all, current divides. Total parallel resistance is always less than the smallest branch.
Series: R_total = R₁+R₂+…
Parallel: 1/R = 1/R₁+1/R₂+… | 2R: R=R₁R₂/(R₁+R₂)
Parallel: 1/R = 1/R₁+1/R₂+… | 2R: R=R₁R₂/(R₁+R₂)
Temperature Effect on Resistance
Resistance of metal conductors increases with temperature (positive temperature coefficient). Critical for cable sizing at operating temperature and motor protection.
R_T = R₂₀[1 + α(T−20)]
αCu = 0.00393/°C | αAl = 0.00403/°C
αCu = 0.00393/°C | αAl = 0.00403/°C
🧲Electromagnetism Basics
Faraday's Law
A changing magnetic flux induces an EMF in a conductor. This is the principle behind generators, transformers, and induction motors. The induced EMF opposes the change (Lenz's Law).
e = −N × dΦ/dt | N=turns, Φ=flux (Wb)
Inductance & Capacitance
Inductors store energy in magnetic fields and oppose current change. Capacitors store energy in electric fields and oppose voltage change. Both create reactance in AC circuits.
V_L = L·dI/dt | E_L = ½LI²
I_C = C·dV/dt | E_C = ½CV²
I_C = C·dV/dt | E_C = ½CV²
📐Kirchhoff's Laws
KCL — Current Law
At any node, the algebraic sum of all currents is zero. Current in = current out. Basis of nodal analysis. Based on conservation of electric charge.
ΣI_in = ΣI_out | ΣI = 0 at a node
KVL — Voltage Law
Around any closed loop, the sum of EMFs equals the sum of voltage drops. Basis of mesh analysis. Based on conservation of energy.
ΣV_EMF = ΣI×R | ΣV = 0 around any loop
Thévenin & Norton Theorems
Any linear circuit can be replaced by a simple equivalent. Thévenin: V_th in series with R_th. Norton: I_N in parallel with R_N. Essential for load analysis.
V_th = V_oc | R_th = V_oc/I_sc
I_N = I_sc | R_N = R_th
I_N = I_sc | R_N = R_th
🔢SI Units & Prefixes
Key Electrical Units
Understanding units prevents errors. Always check dimensional consistency before applying any formula. Note: VA and W are numerically equal but conceptually different.
V · A · Ω · W · VA · VAr · Hz · F · H
Ω=V/A | W=V·A | F=C/V | H=V·s/A
Ω=V/A | W=V·A | F=C/V | H=V·s/A
Engineering Prefixes
Metric prefixes essential in electrical engineering practice. Memorise pico to giga.
p=10⁻¹² · n=10⁻⁹ · µ=10⁻⁶ · m=10⁻³
k=10³ · M=10⁶ · G=10⁹
6.3 kV=6300 V | 150 µF=0.00015 F
k=10³ · M=10⁶ · G=10⁹
6.3 kV=6300 V | 150 µF=0.00015 F
〜AC Fundamentals
Sinusoidal Quantities & RMS
AC quantities vary sinusoidally. RMS (Root Mean Square) is the DC-equivalent value used for power calculations. Peak = √2 × RMS for a pure sine wave.
v(t) = Vm·sin(ωt+φ) | V_rms = Vm/√2
ω = 2πf | T = 1/f | f=50 Hz (IEC), 60 Hz (NEC)
ω = 2πf | T = 1/f | f=50 Hz (IEC), 60 Hz (NEC)
Reactance & Impedance
Inductive reactance XL increases with frequency (current lags voltage). Capacitive reactance Xc decreases with frequency (current leads voltage). Impedance Z combines R and X.
XL = 2πfL | Xc = 1/(2πfC)
Z = R + j(XL−Xc) | |Z| = √(R²+(XL−Xc)²)
Z = R + j(XL−Xc) | |Z| = √(R²+(XL−Xc)²)
Power Factor
PF = cosφ — ratio of real to apparent power. Lagging PF (inductive loads like motors) wastes reactive power in cables. PF correction capacitors reduce reactive power draw.
PF = cosφ = P/S
P = S·cosφ (W) | Q = S·sinφ (VAr) | S = √(P²+Q²)
P = S·cosφ (W) | Q = S·sinφ (VAr) | S = √(P²+Q²)
🔺Three-Phase Systems
Why Three-Phase?
Three-phase uses 3 conductors with currents 120° apart. More efficient than single-phase (less conductor material for same power), constant instantaneous power delivery, and creates self-starting rotating magnetic field for motors.
V_line = √3 × V_phase ≈ 1.732 × V_phase
Star: I_line=I_phase | Delta: I_phase=I_line/√3
Star: I_line=I_phase | Delta: I_phase=I_line/√3
Three-Phase Power
The same apparent power formula applies to both star and delta using line values. A 415V, 3-phase, 100A load has S = √3×415×100 ≈ 71.9 kVA.
S = √3·VL·IL (VA)
P = √3·VL·IL·cosφ (W) | Q = √3·VL·IL·sinφ (VAr)
P = √3·VL·IL·cosφ (W) | Q = √3·VL·IL·sinφ (VAr)
Star–Delta (Y–Δ) Connection
Star: neutral available, V_phase = V_line/√3. Delta: no neutral, V_phase = V_line. Motor windings in star for starting (lower voltage per winding), switched to delta at run speed.
Y: V_ph=VL/√3 · I_ph=IL
Δ: V_ph=VL · I_ph=IL/√3
Δ: V_ph=VL · I_ph=IL/√3
⚙️Induction Motors
Operating Principle & Slip
The stator creates a rotating magnetic field at synchronous speed. This induces currents in the rotor, which produce torque. The rotor always runs slightly slower — this difference is slip. Typical slip at full load: 2–5%.
Ns = 60f/p (RPM, p=pole pairs)
slip s = (Ns−N)/Ns | typical s=2–5% at full load
slip s = (Ns−N)/Ns | typical s=2–5% at full load
Full-Load Current & Torque
FLC is used to select cables, fuses, and overload relays. Torque is calculated from shaft power and rotational speed. Breakdown torque ≈ 2–3× rated torque — load must never exceed this.
IL = P_out/(√3·VL·η·cosφ)
T = P/(2πN/60) N·m | I_start(DOL) ≈ 5–7×FLC
T = P/(2πN/60) N·m | I_start(DOL) ≈ 5–7×FLC
Starting Methods
DOL: full starting current (5–7× FLC), simple. Star-Delta: reduces starting current to 1/3. Soft starter: smooth ramp, 2–3× FLC. VFD: full speed/torque control, most flexible.
DOL: I_st=5–7×FLC
Y-Δ: I_st = DOL×(1/3) | VFD: I_st=1–1.5×FLC
Y-Δ: I_st = DOL×(1/3) | VFD: I_st=1–1.5×FLC
🔁Transformers
Operating Principle & Turns Ratio
AC in the primary winding creates a changing flux in the core, inducing EMF in the secondary. No electrical connection — energy is transferred magnetically. Turns ratio sets the voltage transformation.
V1/V2 = N1/N2 = a (turns ratio)
I1/I2 = 1/a | V1·I1 ≈ V2·I2 (ideal)
I1/I2 = 1/a | V1·I1 ≈ V2·I2 (ideal)
Efficiency & Losses
Core losses (P_fe — constant) and copper losses (P_cu — proportional to I²). Maximum efficiency when iron losses = copper losses. Modern power transformers: 98–99.5% efficient.
η = x·S·cosφ / (x·S·cosφ + Pfe + x²·Pcu)
Max η at: x = √(Pfe/Pcu)
Max η at: x = √(Pfe/Pcu)
%Z & Short-Circuit Current
%Z (percentage impedance) determines fault current contribution. Lower %Z → higher fault current. Typical distribution transformers: 4–6% Z. Used in IEC 60909 fault calculations.
Isc = I_rated / (Z%/100)
VR ≈ R%·cosφ ± X%·sinφ | typical Z%=4–6%
VR ≈ R%·cosφ ± X%·sinφ | typical Z%=4–6%
🔌Cable Theory
Conductor Resistance & Material
Resistance depends on material, CSA, and length. Copper (lower ρ) is preferred for power but aluminium is cheaper and lighter. Larger CSA = lower resistance = less voltage drop and heating.
R = ρ·L/A
ρCu=1.72×10⁻⁸ Ω·m | ρAl=2.82×10⁻⁸ Ω·m
ρCu=1.72×10⁻⁸ Ω·m | ρAl=2.82×10⁻⁸ Ω·m
Voltage Drop Limits
IEC 60364 allows max 5% VD from supply to load terminals. Higher VD causes motor overheating, lamp flickering, and equipment malfunction. Calculate for both operating current and starting current.
1φ: ΔV = 2·I·(R·cosφ + X·sinφ)
3φ: ΔV = √3·I·(R·cosφ + X·sinφ)
3φ: ΔV = √3·I·(R·cosφ + X·sinφ)
Derating Factors
Tabulated cable ratings assume specific conditions. Apply correction factors for ambient temperature above 30°C, cables in groups or bunches, and buried installation. I_design ≤ I_z (after all derating).
Iz_derated = Iz_table × k_temp × k_group × k_install
I_design ≤ Iz_derated
I_design ≤ Iz_derated
🔬Cable Testing Theory
Insulation Resistance (IR / Megger)
Applies DC voltage (500V–5kV typically) and measures leakage current. Detects moisture, contamination, insulation degradation. Rule of thumb minimum: (rated kV + 1) MΩ per km. Always discharge cable after test!
IR_min ≈ (U_rated_kV + 1) MΩ/km
Good: >100 MΩ | Suspect: 1–10 MΩ | Fail: <1 MΩ
Good: >100 MΩ | Suspect: 1–10 MΩ | Fail: <1 MΩ
Hi-Pot (Withstand) Test
Applies elevated voltage to verify insulation integrity. AC hi-pot is preferred for XLPE — DC creates space charge in XLPE causing long-term damage. VLF (0.1 Hz) is the best compromise for site testing XLPE cables.
AC site: U_test = 2×Uo, 60 min
VLF: 1.73–2×Uo, 60 min | DC: 3–4×Uo, 15 min (legacy)
VLF: 1.73–2×Uo, 60 min | DC: 3–4×Uo, 15 min (legacy)
Partial Discharge (PD) Test
Detects internal voids, contamination, or electrical treeing in insulation. Measured in picocoulombs (pC). Required for cables >6 kV per IEC 60502-2. PD-free = high quality insulation.
PD test at: 1.73×Uo
Acceptance (XLPE): typically <10 pC
IEC 60502-2: PD test mandatory >3.6/6 kV
Acceptance (XLPE): typically <10 pC
IEC 60502-2: PD test mandatory >3.6/6 kV
🛡Protection Fundamentals
Short Circuit Protection
Short circuits create very high fault currents in milliseconds. Breaking capacity of MCB/MCCB must exceed the prospective short circuit current (PSCC) at the point of installation. IEC 60909 calculates the maximum symmetrical fault current.
Isc3 = c·Vn / (√3·|Z_total|)
c=1.05 (LV max) | Ip = κ·√2·Isc (peak)
κ = 1.02 + 0.98·e^(−3/XR)
c=1.05 (LV max) | Ip = κ·√2·Isc (peak)
κ = 1.02 + 0.98·e^(−3/XR)
Overload Protection
Overloads cause gradual insulation heating. Thermal overload relays protect motors; MCBs with thermal-magnetic characteristic protect cables. Set overload relay at 100–115% FLC for motors.
I_trip ≤ 1.45 × Iz (cable)
Motor OL: 1.0–1.1 × FLC | NEC 430: 125% × FLC
Motor OL: 1.0–1.1 × FLC | NEC 430: 125% × FLC
RCD / Earth Fault
RCDs detect imbalance between line and neutral. 30 mA for personal protection, 300 mA for fire protection. Response time <40 ms at 5× rated current. Mandatory in bathrooms, outdoors, construction sites.
30 mA RCD: personal protection
300 mA: fire protection | 1 A: equipment
Touch voltage limit: 50 V AC (IEC 60364)
300 mA: fire protection | 1 A: equipment
Touch voltage limit: 50 V AC (IEC 60364)
🌍Earthing Systems (IEC 60364)
TN, TT, IT Systems
First letter = supply earth connection. Second letter = equipment earth connection. TN-S most common in new industrial installations. TT common in rural/domestic. IT used in hospitals and uninterruptible processes.
TN-S: separate N and PE throughout
TN-C-S: combined PEN, then split (PME)
TT: separate earth electrode | IT: isolated
TN-C-S: combined PEN, then split (PME)
TT: separate earth electrode | IT: isolated
Equipotential Bonding
Main bonding connects all metallic services (gas, water, structural steel) to the main earthing terminal. Prevents dangerous potential differences during earth faults. Supplementary bonding required in bathrooms.
Main bonding: min 6 mm² Cu
Supplementary: min 2.5 mm² (protected)
Goal: V_touch < 50 V during fault
Supplementary: min 2.5 mm² (protected)
Goal: V_touch < 50 V during fault
Protection Coordination (Selectivity)
Discrimination ensures only the nearest upstream device trips. Time-current curves of downstream and upstream devices must not overlap at the fault level. Zone interlocking used for bus-bar protection.
I_trip(downstream) < I_trip(upstream)
Min discrimination time: 0.1s (electronic)
0.3s (electromechanical relay)
Min discrimination time: 0.1s (electronic)
0.3s (electromechanical relay)
📋Conductor Properties at 20°C
| Conductor | ρ (Ω·m) | α (1/°C) | Density (g/cm³) | Max Temp (XLPE/PVC) | Notes |
|---|---|---|---|---|---|
| Copper (Cu) | 1.72×10⁻⁸ | 0.00393 | 8.96 | 90°C / 70°C | Standard power cable conductor |
| Aluminium (Al) | 2.82×10⁻⁸ | 0.00403 | 2.70 | 90°C / 70°C | Lighter, 1.64× higher ρ than Cu |
| Cu at 75°C | 2.15×10⁻⁸ | — | — | — | IEC/NEC standard for VD calcs |
| Silver (Ag) | 1.59×10⁻⁸ | 0.00380 | 10.5 | — | Best conductor, too costly |
📋Cable CSA vs Indicative Current Rating (Cu XLPE, In Air 30°C — IEC 60364)
| CSA (mm²) | 1-Phase (A) | 3-Phase (A) | R (mΩ/m, Cu) | Typical Application |
|---|---|---|---|---|
| 1.5 | 18 | 16 | 12.1 | Lighting, small appliances |
| 2.5 | 24 | 22 | 7.41 | Sockets, small motors |
| 4 | 32 | 30 | 4.61 | Cookers, A/C units |
| 6 | 41 | 37 | 3.08 | Sub-mains |
| 10 | 57 | 52 | 1.83 | Distribution boards |
| 16 | 76 | 69 | 1.15 | Sub-main feeders |
| 25 | 101 | 90 | 0.727 | LV feeders, large motors |
| 35 | 125 | 110 | 0.524 | Main distribution |
| 50 | 151 | 133 | 0.387 | Main feeders |
| 70 | 192 | 168 | 0.268 | Main feeders |
| 95 | 232 | 201 | 0.193 | Transformer secondaries |
| 120 | 269 | 232 | 0.153 | HV/MV feeders |
| 150 | 306 | 263 | 0.124 | Large feeders |
| 185 | 354 | 303 | 0.0991 | Transmission feeders |
| 240 | 415 | 352 | 0.0754 | Main HV/MV cables |
| 300 | 472 | 400 | 0.0601 | Large HV cables |
📋Typical Motor Data Reference (IE3, 415V 3-Phase, 50 Hz)
| Rating (kW) | FLC (A) | η (%) | PF | Starting Method |
|---|---|---|---|---|
| 0.37 | 1.0 | 72 | 0.72 | DOL |
| 0.75 | 1.9 | 76 | 0.74 | DOL |
| 1.5 | 3.5 | 80 | 0.76 | DOL |
| 2.2 | 4.9 | 82 | 0.78 | DOL |
| 4.0 | 8.5 | 85 | 0.80 | DOL |
| 7.5 | 15.3 | 88 | 0.82 | DOL or Y-Δ |
| 11 | 22.0 | 89 | 0.83 | Y-Δ |
| 15 | 29.5 | 90 | 0.84 | Y-Δ |
| 22 | 42.5 | 91 | 0.85 | Y-Δ |
| 37 | 70.0 | 92 | 0.86 | Y-Δ or Soft-starter |
| 55 | 102 | 93 | 0.87 | Soft-starter or VFD |
| 75 | 138 | 93.5 | 0.87 | VFD recommended |
🎯Self-Test Quiz — Electrical Engineering Fundamentals
📌Quick Formula Reference
⚡ V=IR | P=VI=I²R=V²/R
〜 S=√3·VL·IL | P=S·cosφ | Q=S·sinφ
🔌 1φ:ΔV=2I(Rcosφ+Xsinφ) | 3φ:ΔV=√3·I(Rcosφ+Xsinφ)
⚙️ Ns=60f/p | IL=P/(√3·VL·η·cosφ)
🔁 a=V1/V2 | Isc=I_rated/(Z%/100)
💥 Isc3=c·Vn/(√3·|Z|) | Ip=κ·√2·Isc
XL=2πfL | Xc=1/(2πfC) | f₀=1/(2π√LC)
R=ρL/A | R_T=R₂₀[1+α(T-20)]
〜 S=√3·VL·IL | P=S·cosφ | Q=S·sinφ
🔌 1φ:ΔV=2I(Rcosφ+Xsinφ) | 3φ:ΔV=√3·I(Rcosφ+Xsinφ)
⚙️ Ns=60f/p | IL=P/(√3·VL·η·cosφ)
🔁 a=V1/V2 | Isc=I_rated/(Z%/100)
💥 Isc3=c·Vn/(√3·|Z|) | Ip=κ·√2·Isc
XL=2πfL | Xc=1/(2πfC) | f₀=1/(2π√LC)
R=ρL/A | R_T=R₂₀[1+α(T-20)]
🔬 HV test (XLPE site): 2×Uo, 60 min
VLF: 1.73–2×Uo | DC legacy: 3–4×Uo/15 min
IR_min ≈ (Uo+1) MΩ/km
PD test: 1.73×Uo | limit: <10 pC (XLPE)
VLF: 1.73–2×Uo | DC legacy: 3–4×Uo/15 min
IR_min ≈ (Uo+1) MΩ/km
PD test: 1.73×Uo | limit: <10 pC (XLPE)