ELC-00 · laboratory
Ohm, Kirchhoff, RLC, transformers, skin effect and three-phase power.
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38 governing sheets
V = I R for a metallic resistor at fixed temperature.
CircuitsVout = Vin R2 /(R1+R2) from KVL and Ohm.
Circuitsω0 = 1/√(LC), Q = (1/R)√(L/C).
AC circuitsVs/Vp = Ns/Np = Ip/Is.
Machinesδ = √(2 ρ /(ω μ)) in a linear conductor.
ElectromagneticsP = √3 VL IL cos φ for a balanced system.
Power systemsP = I² R = V² / R dissipated as heat.
LossesU = ½ C V² = ½ Q V.
Energy storageΣ Vk = 0 around a closed loop. KVL is Faraday at zero flux.
CircuitsErms = 4.44 f N Φmax for a sinusoidal flux.
Powerδ = √(2ρ / ωμ) = √(ρ / π f μ). AC current hugs the surface.
FieldsP = √3 VL IL cosφ. Balanced three-wire, line quantities.
PowerP = V I cosφ, Q = V I sinφ, S = V I. Single-phase rms.
PowerU = ½ L I² stored in the magnetic field of an inductor.
Energyi = C dv/dt. Current is capacitance times the voltage slope.
CircuitsB = μ I /(2π r) around a long straight wire.
Magneticsε = −N ΔΦ/Δt. A changing flux through N turns.
FieldsB = μ0 n I inside a long solenoid, n = N/ℓ.
MagneticsId = ε A dE/dt. The missing current that closes Ampère in a charging capacitor.
Fieldspf = P/S = cosφ for linear sinusoidal loads.
PowerΔV ≈ I (R cosφ + X sinφ) per phase. Approximate phasor drop.
PowerIsc = V / Z with Z = √(R²+X²). The bolted-fault current.
PowerΣ Ik = 0 at a node. Charge is conserved.
Circuitsv = L di/dt. Dual of the capacitor law i = C dv/dt.
CircuitsZ = √(R² + (ωL − 1/ωC)²). Minimum at resonance.
Circuitsv(t) = V∞ + (V0−V∞) e^{−t/τ} with τ = R C. Charging or discharging.
CircuitsLoad current of the Thévenin equivalent.
CircuitsNorton source from Thévenin.
CircuitsMatched-load power.
CircuitsOhmic dissipation.
CircuitsStored electric energy.
CircuitsResistive divider.
CircuitsBalanced wye-delta.
CircuitsNatural LC frequency.
CircuitsSharpness of series resonance.
CircuitsMagnetomotive force.
CircuitsV = I R. The linear constitutive law of a resistor.
Circuitsω0 = 1/√(LC). The undamped natural frequency of a series tank.
Circuits