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Formulas that cover 90% of bench work all Ohm's law V = I × R Power P = V × I = V²/R = I²R Voltage divider Vout = Vin × R₂ / (R₁ + R₂) Current divider (2 branches) I₁ = I × R₂ / (R₁ + R₂) LED resistor R = (Vs − Vf) / If RC time constant τ = R × C (full charge ≈ 5τ) RL time constant τ = L / R RC cutoff frequency f = 1 / (2πRC) Resistors in series R = R₁ + R₂ + … Resistors in parallel R = 1 / (1/R₁ + 1/R₂ + …) Capacitors in parallel C = C₁ + C₂ + … Capacitors in series C = 1 / (1/C₁ + 1/C₂ + …) Capacitive reactance Xc = 1 / (2πfC) Inductive reactance Xl = 2πfL
AC circuits & signals — the exam layer all RMS ↔ peak (sine) Vrms = Vp / √2 ≈ 0.707 Vp Average (sine, half cycle) Vavg = 2Vp / π ≈ 0.637 Vp Series RLC impedance Z = √(R² + (Xl − Xc)²) Resonant frequency f₀ = 1 / (2π√(LC)) Q factor (series) Q = (1/R) × √(L/C) Real power P = V × I × cos φ Reactive / apparent power Q = VI sin φ, S² = P² + Q² Capacitor energy E = ½ C V² Inductor energy E = ½ L I² Decibels dB = 20 log(V₂/V₁) = 10 log(P₂/P₁) Op-amp inverting gain Av = −Rf / Rin Op-amp non-inverting gain Av = 1 + Rf / R₁ 555 astable frequency f = 1.44 / ((R₁ + 2R₂) × C) Wavelength λ (m) = 300 / f (MHz)
Machines & power — the exam layer all Synchronous speed Ns = 120f / P Slip s = (Ns − N) / Ns Transformer EMF equation E = 4.44 × f × N × Φm Transformer ratio V₁/V₂ = N₁/N₂ = I₂/I₁ DC machine EMF E = P Φ Z N / 60A Torque from power T (N·m) = 9.55 × P(W) / N(RPM) Three-phase power P = √3 × VL × IL × cos φ Star connection VL = √3 Vph, IL = Iph Delta connection VL = Vph, IL = √3 Iph Efficiency η = Pout / Pin × 100% Energy (units) kWh = kW × hours (1 unit = 1 kWh) Horsepower 1 HP = 746 W Illumination at a point E = (I / d²) × cos θ Magnetic circuit (Hopkinson) MMF = Φ × S = N × I
The foundation all Laws of resistance R = ρ × L / A Watt's law P = V × I = I²R = V²/R Joule's law of heating H = I² × R × t Capacitor charge law Q = C × V, i = C·dv/dt, E = ½CV² Self-induction law v = L × di/dt, E = ½LI²
Circuit analysis — Kirchhoff's laws all Kirchhoff's current law (KCL) ΣI(in) = ΣI(out) Kirchhoff's voltage law (KVL) ΣV(loop) = 0
Charge & electric fields all Coulomb's law F = k × q₁q₂ / r² Gauss's law Φ(E) = Q(enc) / ε₀ Gauss's law for magnetism Φ(B) = 0 (∮ B · dA = 0)
Electromagnetism & induction all Ampère's circuital law ∮ B · dl = μ₀ × I(enc) Biot–Savart law dB = (μ₀/4π) × I (dl × r̂) / r² Ampère's force law F/l = μ₀ × I₁I₂ / (2πd) Faraday's law of induction EMF = −N × dΦ/dt Lenz's law the minus sign in EMF = −N × dΦ/dt Lorentz force law F = q(E + v × B) Fleming's left-hand & right-hand rules F = B × I × L × sin θ Hopkinson's law MMF = Φ × S, S = l / (μ₀μᵣA)
Electrolysis — Faraday's chemical laws all Faraday's first law of electrolysis m = Z × I × t Faraday's second law of electrolysis m₁ / m₂ = E₁ / E₂
Laws of illumination all Inverse square law of illumination E = I / d² Lambert's cosine law E = (I / d²) × cos θ
Solve all Circuit Solver R_series = R₁ + R₂ + … ; 1/R_parallel = 1/R₁ + 1/R₂ + … ; I = V / R_total
Basics all Electrical Power P = V × I = I² × R = V² / R Resistivity R = ρ × L / A Joule Heating H = I² × R × t Reverse Voltage Divider R₂ / (R₁ + R₂) = V_out / V_in Series and Parallel Resistance Series: R = R₁ + R₂ + … | Parallel: 1/R = 1/R₁ + 1/R₂ + … (capacitors are the reverse)
Networks all Kirchhoff's Laws KCL: ΣI_in = ΣI_out | KVL: ΣV around any closed loop = 0 Star-Delta Conversion Δ→Y: R_a = (R_ab × R_ca) / (R_ab + R_bc + R_ca) | Y→Δ: R_ab = R_a + R_b + (R_a R_b / R_c) Wheatstone Bridge At balance: P / Q = R / X → X = (Q × R) / P Thévenin and Norton Equivalent V_th = open-circuit voltage ; R_th = resistance with sources removed ; I_N = V_th / R_th
AC & Power all Capacitive and Inductive Reactance X_C = 1 / (2πfC) ; X_L = 2πfL LC Resonance f₀ = 1 / (2π√(LC)) ; Z₀ = √(L/C) ; Q = Z₀/R ; BW = f₀/Q RLC Impedance Z = √(R² + (X_L − X_C)²) ; φ = arctan((X_L − X_C) / R) Power Triangle S² = P² + Q² ; P = S × cos φ ; pf = P / S 3 Phase Power S = √3 × V_L × I_L ; P = S × cos φ ; Star: V_ph = V_L/√3, I_ph = I_L ; Delta: V_ph = V_L, I_ph = I_L/√3 Transformer Turns Ratio N_p / N_s = V_p / V_s = I_s / I_p Power Factor Correction Q_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf) RMS, Average and Form Factor Sine wave: V_rms = V_peak / √2 ; V_avg = 0.637 × V_peak ; form factor = V_rms / V_avg
Machines all Synchronous Speed and Slip N_s = 120f / P ; s = (N_s − N_r) / N_s ; f_r = s × f Transformer Efficiency & Regulation η = P_out / (P_out + P_iron + P_copper) ; Regulation % = (V_no-load − V_full-load) / V_full-load × 100
EM & Fields all Faraday's Law EMF e = −N × (dΦ / dt) Magnetic Force F = B × I × L × sin θ (conductor) ; F = q × v × B × sin θ (moving charge) Magnetic Circuit MMF = N × I ; S = l / (µ₀µ_r A) ; Φ = MMF / S ; B = Φ / A
Measurements all Ammeter Shunt & Voltmeter Multiplier Shunt: R_sh = (I_g × R_g) / (I − I_g) ; Multiplier: R_s = (V / I_g) − R_g
Electronics all 555 Timer Astable: t_high = 0.693(R₁+R₂)C, t_low = 0.693 R₂C, f = 1/(t_high+t_low) | Monostable: t = 1.1 R C Op-Amp Gain Inverting: A_v = −R_f / R_in | Non-inverting: A_v = 1 + R_f / R_in BJT Base Resistor I_b(min) = I_c / h_FE ; R_b = (V_drive − V_be) / (overdrive × I_b(min)) Zener Diode Regulator R_s = (V_in − V_z) / (I_load + I_z(min)) ; P_z(max) = V_z × (I_R − I_load(min)) Rectifier Half-wave: V_dc = V_pk/π ; Full-wave: V_dc = 2V_pk/π ; Ripple: V_r ≈ I_dc / (f_ripple × C) Capacitor and Inductor Stored Energy E = ½ × C × V² (capacitor) ; E = ½ × L × I² (inductor) ; Q = C × V
Digital all Number Base Converter Positional notation: value = Σ dᵢ × baseⁱ
Everyday all Energy and Electricity Bill Units (kWh) = (Watts / 1000) × hours ; Cost = units × rate Resistor Colour Code Value = (digit bands) × 10^multiplier, ± tolerance band Capacitor Code Value in pF = (first two digits) × 10^(third digit) SMD Resistor Code 3/4-digit: value = (leading digits) × 10^(last digit) ; EIA-96: value = lookup(2 digits) × letter multiplier Component Substitute Checker at-least: candidate ≥ original | at-most: candidate ≤ original | match: within ± tolerance | exact: must be equal Battery Life Runtime (h) = (Capacity in mAh / Load in mA) × derating factor Wire Voltage Drop R_cable = ρ × (2 × L) / A ; V_drop = I × R_cable Illumination E = I / d² ; tilted surface: E = (I / d²) × cos θ
Installation & sizing all Motor Full Load Current I = kW × 1000 / (√3 × V × η × cos φ) [three phase] HP to kW Converter & Formula kW = hp × 0.7355 (metric) | kW = hp × 0.7457 (mechanical) kVA to Amps I = kVA × 1000 / (√3 × V) [three phase] | I = kVA × 1000 / V [single phase] Cable Size I_z = I_table × k_ambient × k_grouping ; V_drop = √3 × I × ρL/A [three phase] MCB & RCCB Selection I_b ≤ I_n ≤ I_z Earthing Conductor Size S = √(I² t) / k ; table rule: S ≤ 16 → S, 16–35 → 16, above 35 → S/2 Electricity Bill Bill = Σ(units in each slab × that slab's rate) + fixed charge × sanctioned kW + duty
Academic all VTU SGPA, CGPA & Percentage SGPA = Σ(Cᵢ × Gᵢ) / ΣCᵢ ; CGPA = Σ(Cₛ × SGPAₛ) / ΣCₛ VTU SEE Marks Needed SEE needed = max(40 % of SEE max, 40 % of total − CIE) Attendance Attendance % = (attended / total) × 100 ; classes needed n: (attended + n) / (total + n) ≥ 0.75