Maharashtra HSC Electrical Technology (Vocational) cheat sheet

Ohm's law: V = I × R; power P = V × I = I²R = V²/R. In a purely resistive circuit current and voltage stay in phase.

Series circuit: same current through all elements, R_total = R1 + R2 + …; voltage divides in proportion to resistance.

Parallel circuit: same voltage across all branches, 1/R_total = 1/R1 + 1/R2 + …; current divides inversely with resistance.

Kirchhoff's current law: algebraic sum of currents at a node is zero (sum in = sum out). Kirchhoff's voltage law: algebraic sum of EMFs and drops around a closed loop is zero.

AC quantities: RMS = peak/√2 for a sine wave; average over a full cycle is zero; form factor = RMS/average = 1.11 for a sine wave.

Frequency f = 1/T and angular frequency ω = 2πf. In India the supply is 230 V single-phase, 50 Hz.

Inductive reactance X_L = 2πfL; capacitive reactance X_C = 1/(2πfC); impedance Z = √(R² + (X_L − X_C)²).

Resistance rises with temperature for metals (positive temperature coefficient); resistivity ρ = RA/L, so R = ρL/A.

Power factor = cos φ = R/Z; real power P = VI cos φ, reactive power Q = VI sin φ, apparent power S = VI in VA.

Copper has resistivity about 1.72 × 10⁻⁸ Ω·m; aluminium about 2.83 × 10⁻⁸ Ω·m. Aluminium is lighter and cheaper but needs about 1.6 times the copper area for equal resistance.

Conductors: copper, aluminium, silver (best conductivity). Insulators: PVC, rubber, porcelain, bakelite, mica.

PVC insulation is rated typically 70 °C continuous; XLPE and butyl rubber allow higher conductor temperatures, so they carry more current for the same size.

Fuse wire is made of tinned copper or an alloy with a low melting point; it must be rated slightly above the circuit's normal current but below the cable's current capacity.

Wiring systems: cleat, casing-and-capping, batten, conduit (surface or concealed), and cable tray. Concealed conduit is preferred in masonry buildings for mechanical protection.

Standard Indian conductor sizes (mm²): 1, 1.5, 2.5, 4, 6, 10, 16, 25, 35, 50, 70, 95. Lighting sub-circuits usually use 1.5 mm²; power sockets 2.5 mm² or larger.

A single-phase circuit is normally limited to about 800 W per sub-circuit for lighting; a 15 A power circuit may feed one or two socket outlets.

Bending radius of a conduit should be at least about 6 times its outer diameter; conduit fill should not exceed roughly 40 % of the internal area.

Cable colour convention (Indian practice): red/yellow/blue for three phases, black for neutral, green for earth.

Transformer EMF equation: E = 4.44 f N Φ_m, where Φ_m is the peak flux. Voltage per turn is the same on both windings, so V1/V2 = N1/N2 = I2/I1.

A transformer works only on AC. Core loss (hysteresis + eddy current) is nearly constant at fixed voltage and frequency; copper loss varies as I².

Efficiency is maximum when copper loss equals core loss. For a distribution transformer, all-day efficiency weights losses over 24 hours and favours low core loss.

DC motor: back EMF E_b = V − I_a R_a; torque T ∝ Φ I_a; speed N ∝ (V − I_a R_a)/Φ. Series motors give high starting torque; shunt motors give nearly constant speed.

Induction motor synchronous speed N_s = 120f/P; slip s = (N_s − N)/N_s, typically 2–5 % at full load. It is a singly-fed machine and needs no commutator.

Starting methods for squirrel-cage induction motors: direct-on-line (small motors), star-delta (starting current reduced to one-third), autotransformer, and rotor-resistance starting for slip-ring motors.

A capacitor-start single-phase induction motor uses a capacitor in the auxiliary winding to create phase displacement and a rotating field.

Alternator frequency f = PN/120, where N is rpm and P is the number of poles.

Motor protection: overload relay against sustained overcurrent, no-volt release to prevent restart after supply failure, and single-phasing protection for three-phase motors.

Ammeter is connected in series and should have very low resistance; voltmeter is in parallel and should have very high resistance.

A galvanometer is converted to an ammeter by a low shunt resistance in parallel: I/I_g = 1 + G/R_sh. It becomes a voltmeter by a high series resistance: V = I_g(G + R_se).

PMMC instruments measure DC only and deflect linearly; moving-iron instruments work on both AC and DC but have non-linear, compressed scales.

Dynamometer-type instruments serve as wattmeters and transfer instruments because deflection depends on the product of two coil currents.

Induction-type energy meter: the disc speed is proportional to power; the meter constant is revolutions per kWh. Registration error is checked with a standard load and stopwatch.

Wheatstone bridge measures medium resistance; Kelvin double bridge measures very low resistance; megohmmeter (insulation tester) measures insulation resistance in MΩ.

Instrument transformers: a current transformer steps current down for measurement (secondary usually 5 A or 1 A); a potential transformer steps voltage down (secondary usually 110 V).

Errors: loading error from instrument resistance, temperature error, friction, and stray magnetic field. Ayrton shunt extends ammeter range without changing damping.

Digital multimeters have high input impedance (typically 10 MΩ), so they load low-power circuits less than analog moving-coil meters.

Typical Indian transmission voltages: 66, 110, 132, 220, 400 kV AC; distribution at 11 kV, then 415 V three-phase four-wire for consumers.

Transmission at high voltage reduces current for the same power, so I²R line loss and conductor cross-section fall; this is why power is stepped up for long distances.

Supply system: generation, transmission, primary distribution (11 kV), secondary distribution (415/230 V), and consumer service connection.

A distribution transformer steps 11 kV down to 415 V three-phase, giving 240 V phase-to-neutral (commonly quoted as 230 V).

Radial distribution is simple and cheap but has poor reliability; ring main gives two paths and better continuity; interconnected systems improve reliability further.

Voltage drop in a feeder ≈ I × R cos φ + I × X sin φ. Permissible voltage variation at the consumer terminal is generally within ±6 % under Indian regulations.

Power factor improvement uses shunt capacitors; a capacitor bank reduces reactive demand and line current without changing active power.

A transmission line's surge impedance is √(L/C); surge impedance loading indicates the natural power limit of the line.

Earthing of the neutral at the transformer star point provides a return path and limits touch voltage during a fault.

Before any installation work, isolate the supply, prove dead with a tester, and lock off or tag the isolating device.

Lighting sub-circuit wiring: phase through the switch, neutral to the lamp. Switches must always be in the phase conductor, never in neutral.

Earthing conductor size is generally half the phase conductor for small cables, with a minimum of 1.5 mm² for lighting circuits.

Insulation resistance test: apply 500 V DC with a megohmmeter between conductors and earth; a new domestic installation should read at least 1 MΩ.

Continuity and polarity tests confirm correct connections; earth electrode resistance is measured with an earth tester and should be low enough to clear faults quickly.

Motor maintenance: check bearing temperature and lubrication, terminal tightness, insulation resistance, cooling fan and air filters, and vibration.

Common motor faults: single phasing (motor hums and heats), overload, earth fault, shorted winding, and bearing failure.

A starter's thermal overload relay must be set to the motor's full-load current, not to the supply fuse rating.

Preventive maintenance schedule items: tightening terminals, cleaning dust from windings, checking contactor contacts, and recording insulation resistance trends.

Electric shock severity depends on current magnitude, path through the body, and duration. About 30 mA through the body can cause breathing difficulty; 50 mA or more can be fatal.

Body resistance falls sharply when skin is wet, so the same voltage becomes far more dangerous in wet conditions.

First aid for electric shock: switch off or separate the victim using dry insulating material, then call for help and begin CPR if breathing has stopped.

Earthing protects by providing a low-resistance path so protective devices operate quickly and touch voltage stays low.

Types of earthing: pipe earthing (galvanised iron pipe in a coke-and-salt bed) and plate earthing (copper or GI plate buried below ground).

An ELCB/RCCB with 30 mA sensitivity protects people against earth leakage; an MCB protects cables against overload and short circuit but not against small leakage currents.

Fire classes: Class C is for electrical fires. Use dry powder or CO₂ extinguishers; never water on live electrical equipment.

Safe isolation sequence: identify circuit, switch off, lock and tag, test for dead on all conductors, then work.

PPE for electrical work: insulated gloves, safety shoes, helmet, and insulated tools rated for the working voltage.

The National Electrical Code of India (NEC 2011) is published by the Bureau of Indian Standards as SP 30 and covers wiring installations.

IS 732 covers the code of practice for electrical wiring installations; IS 3043 covers earthing; IS 694 covers PVC-insulated cables up to 1100 V.

IS 732 requires that every installation have a main switch and that circuits be protected against overload and short circuit by fuses or circuit breakers.

Indian Electricity Rules 1956 (now the Central Electricity Authority Regulations) set the supply voltage limits and the requirement for an earth connection at every consumer terminal.

Standard supply voltages: 230 V single-phase and 400/415 V three-phase, 50 Hz, with permissible variation of about ±6 % (declared in the supply code).

IS 12640 covers residual current operated circuit breakers; 30 mA is the standard sensitivity for personnel protection.

Colour code for three-phase wiring per Indian practice: red, yellow, blue for phases; black for neutral; green for protective earth.

An MCB's rated breaking capacity (kA) must be at least the prospective short-circuit current at its point of installation.

Cable current ratings must be derated for ambient temperature and grouping; IS 3961 gives the current ratings for aluminium and copper conductors.

Standard electrical symbols: a circle with a cross for a lamp, a switch shown as a break in the line, an earth symbol of three decreasing horizontal lines.

Single-line diagram shows the distribution from the supply point through main switch, distribution board, and sub-circuits; each circuit is one line.

Wiring diagram shows actual connections of switches, lamps, and sockets; a circuit diagram shows the electrical relationship only.

Estimation steps: take off quantities from the drawing, apply wastage allowance, price the materials, then add labour and overheads.

Typical wastage allowances: about 5 % for cable and wire, 3–5 % for conduit accessories, and 2 % for switches.

Conduit length is measured along the run plus fittings; the number of bends and junction boxes must be counted separately.

Lighting circuit load is calculated by summing lamp wattages and dividing by 230 V to get current, then selecting cable size and protective device.

Bill of quantities should list item description, unit (metre, number, point), quantity, rate, and amount, and be signed by the estimator.

A layout drawing locates fittings and switches on the floor plan and shows the point wiring route between them.

Diode: conducts when forward biased above about 0.7 V for silicon (0.3 V for germanium); blocks in reverse up to its peak inverse voltage.

Rectifiers: half-wave gives one pulse per cycle, full-wave gives two; a bridge rectifier needs four diodes and no centre tap. Ripple frequency is 50 Hz for half-wave and 100 Hz for full-wave on a 50 Hz supply.

A Zener diode works in reverse breakdown to give a stable reference voltage; it is used with a series resistor.

BJT: I_C = β I_B; the base-emitter junction is forward biased for active operation. A small base current controls a larger collector current.

SCR (thyristor) latches on when the gate receives a pulse and the anode is positive; it turns off only when the anode current falls below the holding current.

A TRIAC controls AC power in both half cycles and is used in lamp dimmers and fan regulators.

A relay is an electromagnetic switch: coil voltage energises it and contacts switch the load. A flyback diode across the coil suppresses the inductive spike.

A contactor is a heavy-duty relay with main contacts and an auxiliary contact used for latching in motor starters.

Logic basics: AND gives output 1 only when all inputs are 1; OR gives 1 when any input is 1; NOT inverts. A NAND gate is a universal gate.

Wire stripping: remove insulation to the required length without nicking the conductor; use a wire stripper matched to the gauge.

Straight-through joints are made by twisting conductors and soldering, then insulating with tape; a Britannia joint is used for overhead conductors.

Crimping is preferred over soldering for terminals: select the correct lug size, insert fully, and crimp with the proper die.

Continuity test: use a multimeter on the resistance range; a reading near zero ohms confirms a sound connection.

Insulation resistance test at 500 V DC between phase and earth must read at least 1 MΩ before energising a new circuit.

When using a megger, disconnect sensitive equipment and confirm the circuit is dead and isolated before applying the test voltage.

Bench practice: keep the work area dry, use insulated tools, and never work on a live circuit during workshop exercises.

Soldering: heat the joint, apply solder to the joint not the iron, and let it cool without movement to get a shiny joint.

Cable gland and termination: strip the outer sheath to the gland length, fit the gland and shroud, and ensure the earth continuity conductor is connected.