WBBSE Madhyamik Power (Vocational) cheat sheet

Electric current I = Q/t, measured in amperes (A); 1 A = 1 coulomb per second.

Ohm's law: V = IR; power P = VI = I²R = V²/R, in watts.

Ohm's law fails for non-linear devices such as diodes and filament lamps, whose resistance changes with temperature.

Conductor resistance R = ρL/A: proportional to length, inversely proportional to cross-section, and rises with temperature for copper.

Effects of current used in practice: heating (fuse, heater), magnetic (relay, motor), chemical (electrolysis), and physiological (shock).

A current of about 30 mA through the human body can cause respiratory arrest; 50 mA and above can be fatal. Body resistance falls when skin is wet.

Earth-leakage protection: ELCB/RCCB trips at 30 mA residual current within milliseconds; it protects people, not equipment from overload.

First aid for electric shock: switch off the supply, use dry insulating material to separate the victim, then give CPR if breathing has stopped.

Fire classes: Class C is electrical fire; use CO₂ or dry powder, never water, on live electrical equipment.

Series circuit: same current through all elements; R_total = R₁ + R₂ + …; voltage divides in ratio of resistances.

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 voltages around any closed loop is zero.

Thevenin's theorem: any two-terminal linear network equals a voltage source V_th in series with R_th, where V_th is the open-circuit voltage and R_th is the resistance seen with sources killed.

Norton's theorem: equivalent current source I_N in parallel with R_N; I_N is the short-circuit current and R_N = R_th.

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

Capacitive reactance X_C = 1/(2πfC); inductive reactance X_L = 2πfL; 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 in VAR, apparent power S = VI in VA.

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

Lighting circuits use 1.0–1.5 mm² copper; power socket circuits use 2.5–4 mm²; main incoming cable is sized to total load current.

A fuse or MCB is placed only in the phase conductor, never in the neutral or earth.

Earth wire is connected to the metal body of an appliance and to the earth electrode; its resistance should be under about 1 ohm for a good installation.

Two-way stair lighting uses two two-way switches with the common terminals linked by two traveller wires.

A megohmmeter (insulation tester) checks insulation resistance; a healthy domestic installation reads at least 1 MΩ.

Conduit, casing-and-capping, and cleat wiring are the standard methods; concealed conduit is preferred in modern buildings.

Earthing types: pipe earthing and plate earthing; earth electrode depth and moisture determine earth resistance.

Faraday's law: induced emf e = −N dΦ/dt; the emf depends on rate of change of flux linkage and number of turns.

Thermal plant cycle: coal burns, water becomes high-pressure steam, steam drives a turbine coupled to an alternator.

Hydro plant: potential energy of stored water converts to kinetic energy and then to electrical energy through a turbine.

Nuclear plant: controlled fission of U-235 releases heat that raises steam for a turbine; no CO₂ is emitted during operation.

Diesel generator: compression-ignition engine drives an alternator; used for standby and remote locations.

Solar photovoltaic cells convert light directly to electricity by the photovoltaic effect; output is DC and needs an inverter.

Wind turbine output rises with the cube of wind speed: P ∝ v³, so doubling wind speed gives about eight times the power.

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

Transmission is at high voltage to reduce current and hence I²R line loss; distribution is at lower voltage near consumers.

Standard Indian transmission voltages: 66 kV, 132 kV, 220 kV, 400 kV, and 765 kV; distribution at 11 kV, 400 V three-phase, 230 V single-phase.

Three-phase line power P = √3 V_L I_L cos φ.

Star connection: line voltage = √3 × phase voltage, line current = phase current. Delta connection: line current = √3 × phase current, line voltage = phase voltage.

Transmission line losses are reduced by raising voltage, since loss = I²R and I = P/(√3 V cos φ).

A distribution transformer steps 11 kV down to 400/230 V; it is usually delta-star connected to provide a neutral.

Overhead line conductors use ACSR (aluminium conductor steel reinforced) for strength and conductivity.

Skin effect pushes AC current to the conductor surface at high frequency, raising effective resistance.

Transformer emf equation: E = 4.44 f N Φ_max; voltage ratio V₂/V₁ = N₂/N₁ = I₁/I₂.

Transformer losses: copper loss (I²R, varies with load squared) and iron loss (hysteresis plus eddy current, nearly constant).

Ideal transformer has no losses; efficiency = output power / input power × 100%.

DC motor back emf E_b = V − I_a R_a; torque T ∝ Φ I_a.

DC motor types: series (high starting torque, used in cranes), shunt (constant speed, used in lathes), compound (both).

Induction motor slip s = (N_s − N)/N_s; synchronous speed N_s = 120f/P.

Single-phase induction motors are not self-starting; a capacitor or shaded pole provides the starting torque.

Motor starter reduces starting current; a direct-on-line starter suits small motors, star-delta suits larger ones.

A diode conducts when forward biased above about 0.7 V (silicon) and blocks in reverse.

A thyristor (SCR) conducts only after a gate pulse and forward voltage; it turns off when anode current falls below holding current.

Half-wave rectifier: one diode, output ripple high; full-wave bridge: four diodes, ripple frequency twice the supply.

Average output of a full-wave rectifier without filter is about 0.637 V_m; with a capacitor filter it approaches V_m.

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

A chopper converts fixed DC to variable DC; a buck chopper steps voltage down, a boost chopper steps it up.

An inverter converts DC to AC; a UPS uses a rectifier-charger plus inverter and battery.

A transistor works as a switch in cut-off (off) and saturation (on) regions; a relay or optocoupler isolates control from the load.

Solar panel rating is in watts peak (Wp); a 100 Wp panel gives about 100 W at standard test conditions of 1000 W/m² and 25 °C.

A solar home system needs a charge controller to prevent overcharge and deep discharge of the battery.

Solar cell efficiency = electrical output power / incident solar power × 100%; typical commercial panels are 15–22%.

Wind power P = ½ ρ A v³ C_p; the theoretical maximum C_p is 0.593 (Betz limit).

Biogas from anaerobic digestion of cattle dung is mainly methane (about 55–70%) and burns cleanly for cooking or gensets.

Energy conservation: replace incandescent lamps with LED, which use about one-fifth to one-tenth the power for the same light.

A capacitor bank improves power factor, reducing reactive current and line losses in an industrial installation.

Energy audit identifies where energy is used and wasted; it precedes any conservation measure.

Standard safety order: isolate supply, lock and tag, test for dead, then work; treat every circuit as live until proved dead.

Common hand tools: screwdriver, pliers, side cutter, wire stripper, hammer, hacksaw, file, and soldering iron.

A soldering joint is sound when it is shiny and smooth; a dull, grainy joint is a cold joint and must be remade.

Drill bit size for a screw or bolt should match the tap or clearance requirement; use a centre punch before drilling.

Wire stripping length should match the terminal; exposed conductor must not extend beyond the terminal.

Insulation tape is applied over the joint in overlapping turns, never as a substitute for a proper connector.

Bench vice, file, and hacksaw are used for shaping and cutting conduit and metal parts; keep files clean with a file card.

PPE for electrical workshop: insulated gloves, safety shoes, goggles, and helmet; test tools before use.

Ammeter is connected in series, voltmeter in parallel; an ideal ammeter has zero resistance, an ideal voltmeter infinite resistance.

A multimeter selects function and range; set the range above the expected value, and never measure resistance on a live circuit.

A clamp meter measures current without breaking the circuit by sensing the magnetic field around a conductor.

An energy meter (kWh meter) records energy; 1 unit = 1 kWh = 1000 W used for one hour.

Insulation resistance is measured with a megohmmeter at 500 V DC for low-voltage installations.

An oscilloscope displays voltage against time; it shows waveform, amplitude, frequency, and phase.

A wattmeter has a current coil in series and a voltage coil in parallel; it reads true power directly.

Measurement error: accuracy is closeness to true value, precision is repeatability; a meter's error is expressed as a percentage of full-scale reading.

A project report follows: title, aim, apparatus, circuit diagram, procedure, observation table, result, conclusion, and precautions.

A working model must be tested for safety: correct fuse rating, proper earthing, and insulated joints before demonstration.

Record observations in a table with units and repeat readings; take the mean to reduce random error.

Circuit diagrams use standard symbols per IS/IEC; label components and show supply voltage and ratings.

A simple project example: automatic street light using an LDR and relay, with a table of light level versus lamp state.

Documentation should include a cost sheet of components, which doubles as entrepreneurship evidence.

Precautions section must state what could go wrong and how it was prevented, not general advice.

Conclusion should compare the measured result with the expected value and explain any difference.

An entrepreneur identifies an opportunity, arranges resources, and bears risk for profit.

A business plan contains product or service, market, cost, pricing, profit estimate, and risk assessment.

Break-even point is where total revenue equals total cost; units = fixed cost / (selling price − variable cost per unit).

Working capital is the money needed for day-to-day operations; fixed capital is spent on plant and tools.

For a small electrical service business, pricing must cover material, labour, transport, and overhead, plus a margin.

GST registration and a current account are basic compliance steps for a small Indian enterprise.

Employability skills: communication, teamwork, time management, problem solving, and digital literacy.

A resume lists contact details, education, skills, and experience; a cover letter is tailored to the specific job.

Interview preparation: research the employer, prepare examples of work done, and ask relevant questions at the end.