Tamil Nadu HSE Second Year Basic Electrical Engineering cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. In a series circuit current is common and voltages add; in parallel, voltage is common and currents add.

Kirchhoff's laws: KCL states the algebraic sum of currents at a node is zero; KVL states the algebraic sum of EMFs and drops around any closed loop is zero.

Resistors in series add directly (R = R₁ + R₂ + …); in parallel the reciprocals add, and for two resistors R = R₁R₂/(R₁ + R₂).

Conductor resistance R = ρl/A: doubling length doubles resistance; doubling cross-sectional area halves it; temperature rise increases resistance of metals.

Current = rate of charge flow, I = Q/t; one ampere is one coulomb per second. One electron carries 1.602 × 10⁻¹⁹ C.

EMF is the source's open-circuit driving voltage; terminal voltage V = E − Ir, where r is internal resistance, so terminal voltage falls as load current rises.

Energy consumed W = Pt; a 1000 W load running one hour uses 1 kWh (one unit). Energy in joules = watts × seconds.

Maximum power transfer to a load occurs when load resistance equals source internal resistance; efficiency at that point is only 50%.

Star–delta conversion: for equal resistors, R_star = R_delta/3 and R_delta = 3R_star.

Coulomb's law: F = (1/4πε₀)(q₁q₂/r²); force falls with the square of separation and is attractive for unlike charges, repulsive for like charges.

Electric field intensity E = F/q (N/C or V/m); potential V = W/q (volt = joule per coulomb); capacitance C = Q/V in farads.

Parallel-plate capacitance C = ε₀ε_rA/d: capacitance rises with plate area and dielectric constant, falls with plate separation.

Capacitors in parallel add (C = C₁ + C₂); in series the reciprocals add, and the same charge appears on each series capacitor.

Energy stored = ½CV² = ½QV = Q²/2C.

Time constant of an RC circuit is τ = RC seconds; after one τ the capacitor charges to 63.2% of final voltage, after five τ it is effectively full.

Dielectric strength sets breakdown voltage; inserting a dielectric of relative permittivity ε_r multiplies capacitance by ε_r.

In steady DC a capacitor behaves as an open circuit; its reactance X_C = 1/(2πfC) falls as frequency rises.

Magnetic flux Φ in webers; flux density B = Φ/A in tesla (Wb/m²); magnetomotive force F = NI ampere-turns; reluctance opposes flux.

Force on a current-carrying conductor F = BIl sinθ; force on a charge F = qvB sinθ; direction from Fleming's left-hand rule.

Biot–Savart/straight conductor: B = μ₀I/(2πr) at distance r; inside a solenoid B = μ₀NI/l.

Faraday's law: induced EMF e = −N dΦ/dt; the magnitude depends on rate of flux change, turns and flux strength, not on the flux itself.

Lenz's law: the induced current opposes the change producing it - the basis of the minus sign and of back EMF in motors.

Fleming's right-hand rule gives the direction of induced EMF in a generator; left-hand rule gives the direction of motor force.

Self-inductance L in henries; induced EMF e = −L di/dt; energy stored in an inductor = ½LI².

Mutually induced EMF e₂ = −M di₁/dt; coefficient of coupling k = M/√(L₁L₂), with k = 1 for ideal coupling.

Eddy currents are circulating currents in a magnetic core; they are reduced by laminating the core, while hysteresis loss is reduced by using silicon steel.

RMS value = peak/√2 = 0.707 × peak; average value of a full sine wave is zero, and half-cycle average = 0.637 × peak.

Form factor = RMS/average = 1.11 for a sine wave; peak factor = peak/RMS = 1.414.

Frequency f = 1/T and ω = 2πf; in India supply is 230 V single-phase, 50 Hz, and 415 V three-phase.

Inductive reactance X_L = 2πfL (current lags voltage by 90°); capacitive reactance X_C = 1/(2πfC) (current leads by 90°).

Impedance Z = √(R² + (X_L − X_C)²); power factor cos φ = R/Z; true power P = VI cos φ, reactive power Q = VI sin φ, apparent power S = VI.

Resonance in a series RLC circuit occurs at f = 1/(2π√(LC)), where X_L = X_C, Z = R and power factor is unity.

In star connection line voltage = √3 × phase voltage and line current = phase current; in delta, line current = √3 × phase current and line voltage = phase voltage.

Three-phase power P = √3 V_L I_L cos φ; for a balanced load the neutral carries no current.

Power factor correction uses parallel capacitors; low power factor increases current and line losses for the same useful power.

Transformer EMF equation E = 4.44 f N Φ_m; voltage ratio equals turns ratio V₂/V₁ = N₂/N₁, and for an ideal transformer V₁I₁ = V₂I₂.

A transformer works only on AC; it transfers power by mutual induction with no moving parts, and its core is laminated to cut eddy-current loss.

Transformer losses: copper loss (I²R, varies with load squared) and iron loss (hysteresis plus eddy, essentially constant at fixed voltage/frequency).

DC generator EMF E = (ΦZNP)/(60A), where A = P for lap winding and A = 2 for wave winding; E is proportional to flux and speed.

DC motor torque T = 0.159 Φ I Z P/A (N·m) approximately; back EMF E_b = V − I_aR_a, and speed falls as load increases.

DC series motor has high starting torque and must never be started unloaded; shunt motor is nearly constant-speed; compound combines both.

Synchronous motor runs only at synchronous speed N_s = 120f/P; synchronous generator (alternator) frequency f = PN_s/120.

Three-phase induction motor runs below synchronous speed; slip s = (N_s − N)/N_s, rotor frequency = sf, and it is self-starting with a squirrel-cage rotor.

Single-phase induction motors are not self-starting on their own; capacitor-start and split-phase designs create a phase-split starting torque.

Indian wiring colour convention: phase red (or brown), neutral black (or blue), earth green (or green-yellow).

Earth wire is connected to the metal body of appliances so that a fault current blows the fuse or trips the ELCB instead of shocking the user.

Fuse rating is chosen slightly above full-load current; a fuse protects against overload and short circuit but not against small earth leakage.

MCB trips on overload and short circuit and is resettable; ELCB/RCCB with 30 mA sensitivity protects people against earth leakage.

Wire size selection depends on current-carrying capacity, voltage drop (typically kept under about 3–5%) and ambient temperature; 1.5 mm² is common for lighting, 2.5–4 mm² for power sockets.

Domestic circuits are wired in parallel so each load gets full supply voltage and can be switched independently.

Two-way switching of a lamp uses two two-way switches with strapping wires; the intermediate switch extends this to three or more positions.

Earthing resistance should be low (a few ohms); pipe and plate earthing are common, and earth continuity must be tested before energising.

First aid for electric shock: switch off supply, use dry insulating material to separate the victim, then call for medical help; never touch the person while still in contact with live parts.

Ammeter is connected in series and has very low resistance; voltmeter is in parallel and has very high resistance; a wattmeter has both current and potential coils.

Moving-coil instruments respond to average value and work on DC; moving-iron instruments respond to RMS and work on AC and DC.

Damping in indicating instruments is by eddy currents (moving coil), air friction or fluid friction; controlling torque is by spring or gravity.

Extension of range: a shunt (low resistance) across an ammeter; a series multiplier (high resistance) with a voltmeter.

Analog multimeter measures voltage, current and resistance; a digital multimeter gives higher input impedance and direct reading.

Megger (insulation resistance tester) applies a high DC voltage to measure insulation resistance in megohms; a low reading indicates moisture or insulation failure.

Energy meter (kWh meter) measures energy; its constant is revolutions per kWh, so units consumed = revolutions/constant.

Continuity test uses a low-resistance range with the circuit dead; polarity and phase sequence tests confirm correct connection before commissioning.

Instrument error types: systematic (calibration, zero error) and random; accuracy is closeness to true value, precision is repeatability.

Lead-acid cell: about 2 V per cell, electrolyte dilute sulphuric acid, and fully charged specific gravity near 1.28; discharging lowers it.

Batteries in series add voltages with common current capacity; in parallel add current capacity at the same voltage.

Battery capacity in ampere-hours (Ah); life in hours ≈ Ah/load current, and charging current is often set at about one-tenth of Ah capacity.

A diode conducts when forward biased above about 0.7 V (silicon) or 0.3 V (germanium); it blocks in reverse up to its peak inverse voltage.

Half-wave rectifier gives one pulse per cycle with ripple frequency f; full-wave and bridge rectifiers give two pulses per cycle at 2f.

A filter capacitor across the rectifier output smooths ripple; larger capacitance and heavier load current increase ripple.

Zener diode works in reverse breakdown to give a stable reference voltage for regulation; a series resistor limits zener current.

A transistor has emitter, base and collector; in common-emitter configuration it gives voltage and current gain and is used as a switch or amplifier.

SCR (thyristor) conducts only after a gate pulse and turns off when current falls below holding current; it is used for controlled rectification and power control.

Conventional sources: thermal (coal), hydro, nuclear, diesel; non-conventional: solar photovoltaic, wind, biomass, tidal, geothermal.

India's standard generation and transmission voltages include 11 kV generation, 33/66/110/220 kV transmission and 400 kV extra-high voltage; 230 V is the domestic distribution level.

Transmission at high voltage reduces current for the same power, cutting I²R line loss; losses fall with the square of the voltage ratio.

Step-up transformers are used at generating stations and step-down transformers at substations near load centres.

Base load is met by large thermal or nuclear plants; peak load is met by hydro or gas plants that can start quickly.

Solar cell output depends on irradiance and temperature; a PV module's open-circuit voltage falls slightly as cell temperature rises.

Utilization: electric heating uses resistance (P = V²/R); induction and dielectric heating give faster, cleaner heating for industrial use.

Electric traction advantages: high starting torque, no local pollution, regenerative braking; supply is typically 25 kV AC single-phase on Indian Railways.

Illumination: luminous flux in lumens, illuminance in lux (lumens per m²); LED lamps give far higher efficacy (lumens per watt) than incandescent lamps.