WBCHSE HS Vocational Power cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R. In a purely resistive circuit current and voltage are 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 + …; for two resistors R_total = R₁R₂/(R₁+R₂).

Kirchhoff's current law: algebraic sum of currents at a node is zero; Kirchhoff's voltage law: algebraic sum of EMFs and drops around a loop is zero.

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

Resonance occurs when X_L = X_C, giving f_r = 1/(2π√(LC)); at resonance Z is minimum and purely resistive in a series circuit.

Power factor = cos φ = P/S; active power P in watts, reactive power Q in VAR, apparent power S in VA, with S = √(P² + Q²).

Three-phase star connection: V_L = √3 V_ph and I_L = I_ph; delta connection: V_L = V_ph and I_L = √3 I_ph.

Time constant of an RC circuit τ = RC and of an RL circuit τ = L/R; after one τ a quantity reaches about 63% of final value.

Copper resistivity ≈ 1.72 × 10⁻⁸ Ω·m at 20 °C; aluminium ≈ 2.83 × 10⁻⁸ Ω·m - aluminium needs roughly 1.6 times the copper area for equal resistance.

Cable voltage drop ≈ (2 × L × I × ρ)/A for a single-phase two-wire run; permissible drop is commonly limited to about 3–5% of supply voltage.

Standard Indian conductor sizes follow the R-series, e.g. 1.0, 1.5, 2.5, 4, 6, 10, 16, 25, 35 mm²; earth continuity conductor is sized per the phase conductor rating.

Colour convention (Indian practice): phase red/yellow/blue for three phases, black or light blue for neutral, green or green-yellow for protective earth.

PVC cable current rating falls as ambient temperature and grouping (number of circuits bunched) increase; derating factors are applied from cable manufacturer tables.

Bending radius of a PVC-insulated cable is typically not less than about 8–12 times the overall cable diameter to avoid insulation damage.

Conduit fill should not exceed roughly 40% of the internal cross-section; the number of bends between draw boxes should be limited to two 90° bends.

Lighting sub-circuits are commonly wired with 1.5 mm² copper and power sockets with 2.5–4 mm²; a 6 A circuit is typical for lighting and 16 A for power.

Kit-kat fuse and MCB selection: MCB rating must be above design load current but below the cable's current-carrying capacity.

Transformer EMF equation: E = 4.44 f N Φ_m; voltage per turn is the same on primary and secondary.

Ideal transformer relations: V₁/V₂ = N₁/N₂ = I₂/I₁; for a three-phase transformer the √3 factor enters when line quantities are used.

Transformer losses: copper loss varies as I² (load-dependent), core loss is nearly constant at rated voltage and frequency; maximum efficiency occurs when copper loss equals core loss.

DC machine EMF: E = (PΦNZ)/(60A), where P = poles, Z = conductors, N = rpm, A = parallel paths; torque T = 0.159 PΦZI_a/A (N·m with Φ in Wb).

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

Synchronous speed N_s = 120f/P; slip s = (N_s − N_r)/N_s and rotor frequency = s·f.

Induction motor torque is proportional to square of applied voltage; therefore a 10% voltage dip reduces torque by about 19%.

Star-delta starter reduces starting voltage per phase to 1/√3 and starting torque to one-third of direct-on-line value.

Single-phase induction motors are not self-starting; a capacitor or split-phase auxiliary winding provides the rotating field.

Typical Indian generation voltages: thermal/hydro generators at 11 kV or 15.75 kV, stepped up to 132, 220, or 400 kV for transmission.

Transmission line losses for a given power fall as voltage rises because I = P/(√3 V cos φ) and loss = 3I²R.

Standard transmission voltages in India: 66, 110, 132, 220, 400, 765 kV AC; HVDC links use ±500 kV and ±800 kV.

Distribution is normally radial at 11 kV from a substation, then stepped to 415 V three-phase four-wire for consumers.

Load factor = average load / maximum demand; diversity factor = sum of individual maximum demands / maximum demand on the system.

Per-unit system: base quantities chosen as S_base and V_base; Z_base = V_base²/S_base, and per-unit impedance is the same on either side of an ideal transformer.

Ferranti effect: on a long lightly loaded line, receiving-end voltage exceeds sending-end voltage because of line charging capacitance.

Corona loss increases with voltage, conductor surface irregularity, and reduced spacing; it is reduced by bundled conductors and larger conductor diameter.

Skin effect pushes AC current to the conductor surface, raising effective resistance; it becomes significant at high frequency and large conductor size.

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

PMMC instrument measures average value and works only on DC; a rectifier-type moving-iron or dynamometer instrument is used for AC.

Moving-iron instruments measure RMS value; their deflection is proportional to I² (or V²) and they read correctly on AC and DC.

Energy meter constant is expressed in revolutions per kWh; energy = (number of revolutions)/(meter constant).

Wattmeter in a two-wattmeter method for a balanced three-phase load: total power = W₁ + W₂, and power factor = cos[tan⁻¹(√3(W₁ − W₂)/(W₁ + W₂))].

Megger (insulation resistance tester) applies a high DC test voltage; insulation resistance is measured in megohms and typically must exceed 1 MΩ for LV installations.

Continuity test uses a low-resistance ohmmeter or buzzer; earth electrode resistance is measured with a fall-of-potential or earth tester.

Instrument accuracy class, e.g. 0.5 or 1.0, means the error is a percentage of full-scale deflection, not of the reading.

Current transformer (CT) secondary is normally 5 A or 1 A; the secondary must never be open-circuited while primary current flows.

A diode conducts when forward-biased above its knee voltage (~0.7 V for silicon) and blocks in reverse; reverse recovery time limits high-frequency use.

SCR (thyristor) is turned on by a gate pulse when anode is positive; it turns off only when anode current falls below holding current.

Average output of a single-phase half-wave controlled rectifier with resistive load: V_dc = (V_m/2π)(1 + cos α).

Full-wave controlled rectifier (resistive load): V_dc = (V_m/π)(1 + cos α); at α = 0 this gives 0.636 V_m.

TRIAC is a bidirectional thyristor used for AC phase control such as lamp dimmers and small fan regulators; DIAC is often used to trigger it.

IGBT combines MOSFET gate drive with BJT conduction; it is the dominant switch in industrial PWM inverters and VFDs.

PWM inverter output voltage is controlled by modulation index; V/f control keeps air-gap flux constant in induction motor drives.

Buck converter output V_o = D·V_in; boost converter V_o = V_in/(1 − D), where D is duty cycle.

Snubber (RC) circuits across thyristors limit dv/dt and suppress switching overvoltage; a freewheeling diode protects against inductive load spikes.

Body current above about 30 mA through the heart is dangerous; an RCD/ELCB rated 30 mA is used for personnel protection.

Earth loop impedance must be low enough that the protective device trips within the disconnection time; MCB magnetic trip threshold is typically 5–10 × rated current (Type C).

Earthing types: plate earth, pipe earth, rod earth, strip/plate electrode; earth resistance for domestic installations should be kept below about 1–5 Ω depending on supply.

IS 3043 gives the code of practice for earthing; earth conductor size is selected from the phase conductor rating using standard tables.

Class I equipment relies on protective earthing; Class II is double-insulated and does not require an earth connection.

Fuse operates on I²t heating; HRC fuses have high rupturing capacity and are used for motor and distribution protection.

MCB protects against overload and short circuit; MCCB adds adjustable trip settings for higher ratings; ELCB/RCCB detects earth leakage current.

Lockout/tagout (LOTO) before working on a circuit: isolate, lock, tag, prove dead with a tester, and discharge capacitors.

First aid for electric shock: switch off supply, do not touch the casualty until isolated, then start CPR if breathing has stopped.

Electric heating: resistance heating uses I²Rt; induction heating relies on eddy currents; dielectric heating suits non-conducting materials such as PVC and wood.

Electric arc welding uses a step-down transformer with a drooping characteristic; open-circuit voltage is typically 50–90 V and welding current 100–400 A.

Electric traction motors are usually DC series or three-phase induction with VVVF control; tractive effort is proportional to torque.

Illumination: luminous efficacy is expressed in lumens per watt; LED lamps reach 100–150 lm/W compared with ~15 lm/W for incandescent.

Illumination law: E = I/d² for a point source at normal incidence (inverse-square law); E = (I cos θ)/d² for oblique incidence.

Motor selection: continuous duty, short-time, and intermittent duty are the main duty types; service factor indicates permissible overload.

VFD energy saving follows the affinity laws: flow ∝ speed, head ∝ speed², power ∝ speed³ for centrifugal fans and pumps.

Braking of induction motors: plugging reverses phase sequence; dynamic braking applies DC to the stator; regenerative braking returns energy to supply.

Load torque-speed characteristics: constant torque (conveyors), constant power (machine tools), and fan-type (torque ∝ speed²).

Standard hand tools: screwdriver, pliers, side cutter, wire stripper, crimping tool, hacksaw, file, chisel, and bench vice.

Wire stripping should expose only the length needed for the terminal; insulation must not be nicked, and conductor strands must not be cut.

Crimping is preferred over soldering for terminal lugs; the correct die and lug size must match the conductor cross-section.

PVC conduit bending uses a bending spring; the minimum bend radius must not kink the conduit, and joints are made with couplers only at draw points.

Wire joint types: Western Union (for overhead lines), Britannia (straight joint), and tee joint; all must be soldered or crimped and insulated.

Drilling: drill speed is inversely proportional to drill diameter; a centre punch mark prevents the drill from wandering.

Soldering an electrical joint requires a rosin flux cored solder; acid flux must be avoided on copper conductors because it corrodes.

Insulation resistance test after wiring: disconnect loads, apply megger, expect >1 MΩ between conductors and between conductor and earth.

Safe use of ladders and portable tools: verify tool double insulation, use RCD-protected supply, and never work on live circuits without authorization.

Business plan components: market analysis, product/service description, operations plan, financial projections, and risk assessment.

Break-even quantity = fixed cost / (selling price per unit − variable cost per unit); it identifies the minimum sales needed to avoid loss.

Working capital = current assets − current liabilities; it funds day-to-day operations such as wages, materials, and power bills.

GST registration thresholds and rates vary by state and turnover; a small electrical contractor must register once turnover crosses the prescribed limit.

MSME/Udyam registration gives access to subsidized loans, tender preferences, and delayed-payment protection under Indian law.

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

Interview preparation: research the employer, prepare examples using the STAR method (Situation, Task, Action, Result), and ask relevant questions.

Workplace ethics: maintain confidentiality, follow safety rules, report hazards, and respect diversity and anti-harassment policies.

Record keeping for a small electrical business: invoices, purchase bills, warranty documents, test certificates, and statutory licences.