RRB JE CBT 2 Electrical cheat sheet

Ohm's law: V = I × R; power P = V × I = I²R = V²/R. In series circuits, current is common, voltage divides; in parallel, voltage is common, current divides.

Kirchhoff's laws: KCL (sum of currents at a node = 0) and KVL (sum of voltages around a loop = 0). Use for mesh and nodal analysis.

Thevenin's theorem: any linear two-terminal network can be replaced by a voltage source Vth in series with Rth, where Vth is open-circuit voltage and Rth is the resistance seen with sources killed (voltage sources shorted, current sources opened).

Norton's theorem: equivalent current source IN = Vth/Rth in parallel with Rth. Source transformation: Vth in series with R converts to IN = Vth/R in parallel with R.

Superposition: in a linear network with multiple independent sources, the response is the sum of responses from each source acting alone (other sources killed).

Maximum power transfer: load receives maximum power when RL = Rth; maximum power = Vth²/(4Rth), efficiency = 50%.

AC fundamentals: RMS value = peak/√2 for sine; average value = (2/π) × peak; form factor = RMS/average = 1.11; peak factor = peak/RMS = 1.414.

In pure inductance, current lags voltage by 90°; in pure capacitance, current leads voltage by 90°; impedance Z = R + j(XL − XC), where XL = 2πfL and XC = 1/(2πfC).

Faraday's law: e = −N dΦ/dt. Lenz's law: induced emf opposes the change in flux. Self-inductance L = NΦ/I; mutual inductance M = k√(L1L2).

DC generator EMF: E = (PΦNZ)/(60A), where P = poles, Φ = flux per pole, N = speed in rpm, Z = total conductors, A = number of parallel paths (A = 2 for wave winding, A = P for lap winding).

DC motor torque: T = (PΦIZ)/(2πA) N·m; back emf Eb = V − IaRa; speed N ∝ (V − IaRa)/Φ.

DC motor starters are needed because at start Eb = 0, so Ia = V/Ra is very high; a starter inserts external resistance in the armature circuit.

Transformer EMF equation: E = 4.44 f N Φm; voltage per turn is the same in primary and secondary. Turns ratio a = N1/N2 = V1/V2 ≈ I2/I1.

Transformer losses: copper loss varies as (load current)² and is found by short-circuit test; iron loss is constant and found by open-circuit test. Efficiency is maximum when copper loss = iron loss.

Three-phase induction motor: synchronous speed Ns = 120f/P; slip s = (Ns − Nr)/Ns; rotor frequency fr = s f; rotor emf at standstill E2, at slip s is sE2.

Induction motor torque is maximum at slip s = R2/X2 (standstill rotor resistance/reactance). Star-delta starter reduces starting voltage to 1/√3 and starting torque to 1/3.

Synchronous machine: emf equation E = 4.44 f Φ T kd kp; synchronous speed Ns = 120f/P. For a synchronous motor, excitation controls power factor: under-excited draws lagging current, over-excited draws leading current.

Generation: thermal plant efficiency is limited by Rankine cycle; hydro is quick-starting; nuclear uses controlled fission. Base load is supplied by large thermal/nuclear; peak load by hydro/gas.

Transmission line models: short line (<80 km) uses series impedance only; medium line (80–250 km) uses nominal π or T; long line (>250 km) uses distributed parameters. Surge impedance Zc = √(L/C); SIL = V²/Zc.

Corona: occurs when conductor surface voltage gradient exceeds breakdown strength of air (≈30 kV/cm peak). Corona loss increases with frequency and reduces with larger conductor diameter and bundle conductors.

Skin effect: AC current concentrates near conductor surface, increasing effective resistance at higher frequencies; mitigated by stranded conductors.

Per-unit system: choose base power and base voltage; Zpu = Zactual/Zbase; base impedance = (kVbase)²/MVAbase. Per-unit values are independent of voltage level.

Protection: overcurrent relay for overload; distance relay for transmission lines (mho, impedance, reactance); differential relay for transformers and generators; Buchholz relay for oil-immersed transformer gas detection.

Switchgear: circuit breaker arc quenching in SF6 (excellent dielectric), vacuum (for medium voltage), air-blast. Rated breaking capacity must exceed fault level.

Utilization: tariff types (flat rate, block rate, two-part, maximum demand); power factor improvement using shunt capacitors reduces kVA demand and losses.

Indicating instruments: PMMC (permanent-magnet moving-coil) measures DC only; moving iron (MI) measures AC and DC; electrodynamometer measures AC/DC and can be used as transfer instrument.

Ammeter is connected in series and has low resistance; voltmeter is connected in parallel and has high resistance. Extend ammeter range with a shunt; extend voltmeter range with a series multiplier.

Wattmeter: dynamometer type; reading P = V I cos φ. In a three-phase system, two-wattmeter method: total power = W1 + W2; power factor angle φ = tan⁻¹[√3(W1 − W2)/(W1 + W2)].

Energy meter (integrating instrument): induction type; meter constant = revolutions per kWh. Creep is prevented by a brake magnet; friction compensation by a shading coil.

Wheatstone bridge: balance condition R1/R2 = R3/R4; used for medium resistance. Kelvin double bridge for low resistance; Megger for insulation resistance.

Maxwell bridge measures inductance using known capacitance; Hay bridge for high-Q inductance; Schering bridge for capacitance and dielectric loss; Wien bridge for frequency.

Transducers: LVDT (linear variable differential transformer) for displacement; strain gauge for strain (gauge factor ≈ 2); thermistor for temperature (negative temperature coefficient); piezoelectric for pressure/vibration.

Instrument transformers: CT (current transformer) steps down current for measurement; PT (potential transformer) steps down voltage. Burden is the connected load in VA.

Power semiconductor devices: diode (uncontrolled), SCR/thyristor (controlled turn-on, line commutated), TRIAC (bidirectional), GTO (gate turn-off), MOSFET (fast, low voltage), IGBT (high voltage, fast).

SCR: turns on by gate pulse when anode positive with respect to cathode; turns off when anode current falls below holding current (natural commutation) or by forced commutation.

Rectifiers: half-wave single-phase gives average output Vm/π; full-wave gives 2Vm/π; three-phase full-wave gives 3√3 Vm/π. Ripple frequency for p-pulse converter is p × supply frequency.

Choppers: step-down (buck) average output = D × Vin; step-up (boost) = Vin/(1−D); buck-boost inverts. D is duty cycle.

Inverters: convert DC to AC. Single-phase bridge inverter output is quasi-square; PWM control reduces harmonics. Three-phase inverter requires six switches with 120° or 180° conduction.

AC voltage controllers use phase control of thyristors (fan regulator, dimmer). Cycloconverter directly converts fixed AC frequency to variable AC frequency.

DC drives: speed control by armature voltage (below base speed) and field flux (above base speed). Ward-Leonard system uses a motor-generator set for smooth speed control.

Induction motor drives: V/f control maintains constant flux; stator voltage control, rotor resistance control (slip-ring), and variable frequency drives (VFD) are common methods.

Open-loop vs closed-loop: closed-loop has feedback, reduces sensitivity to disturbances, but may be unstable. Transfer function = output/input with zero initial conditions.

First-order system step response: time constant τ = L/R or RC; reaches 63.2% of final value in one τ and 98% in 4τ. Second-order system: damping ratio ζ, natural frequency ωn; underdamped if 0 < ζ < 1.

Routh-Hurwitz criterion: number of sign changes in first column of Routh array equals number of right-half-plane poles. Special cases: zero in first column or zero row.

Bode plot: gain margin = negative of gain at phase crossover; phase margin = 180° + phase at gain crossover. For stable system, both margins should be positive.

Illumination: luminous flux in lumen, illuminance in lux (lm/m²), luminous intensity in candela. Inverse square law: E = I/d². Lambert's cosine law: E = (I cos θ)/d².

Electric heating: resistance heating (direct/indirect), induction heating (eddy currents), dielectric heating (high-frequency electric field for non-conductors), arc heating (electric arc furnace).

Electric welding: arc welding uses low voltage high current; resistance welding uses pressure and current. Welding transformer has low voltage and high current rating with high leakage reactance.

Traction: DC series motor is preferred due to high starting torque. Traction supply is 25 kV AC single-phase (Indian Railways) or 750 V DC third rail. Speed control by series-parallel, field weakening, and tap changer.

Semiconductor devices: PN junction diode conducts when forward biased (barrier potential ≈0.7 V Si, 0.3 V Ge). Zener diode works in reverse breakdown for voltage regulation.

BJT: current-controlled device; β = IC/IB; α = IC/IE; β = α/(1−α). Common-emitter amplifier has voltage gain and 180° phase shift. MOSFET is voltage-controlled.

Operational amplifier: ideal op-amp has infinite open-loop gain, infinite input impedance, zero output impedance. Inverting amplifier gain = −Rf/Rin; non-inverting gain = 1 + Rf/Rin.

Op-amp applications: summing amplifier, integrator, differentiator, comparator, Schmitt trigger, active filters, instrumentation amplifier.

Logic gates: AND, OR, NOT; universal gates NAND and NOR. De Morgan's theorems: (A·B)' = A' + B'; (A+B)' = A'·B'.

Boolean algebra: simplify using K-map; flip-flops (SR, JK, D, T) are bistable; JK flip-flop eliminates race condition; registers and counters use flip-flops.

Microprocessor (e.g., 8085): 8-bit, 16-bit address bus (64 KB), 8-bit data bus. Instruction cycle: fetch, decode, execute. Interrupts: maskable and non-maskable (TRAP is non-maskable in 8085).

Number systems: binary, octal, decimal, hexadecimal; 1's and 2's complement for signed numbers. ASCII and BCD codes; parity bit for error detection.

Indian Railways: headquartered at Rail Bhavan, New Delhi; zones (currently 18) each headed by a General Manager; divisions headed by Divisional Railway Manager (DRM).

Railway Minister is the political head; Railway Board (chaired by Chairman) is the apex administrative body. Research Designs and Standards Organisation (RDSO) is at Lucknow.

Important days: National Science Day 28 February; World Environment Day 5 June; International Yoga Day 21 June; National Sports Day 29 August.

Indian Constitution: adopted 26 November 1949, came into force 26 January 1950; Fundamental Rights in Part III; Directive Principles in Part IV.

Current affairs: read a national newspaper daily; note appointments, awards (Bharat Ratna, Padma awards), sports events, and railway initiatives like Vande Bharat, Kavach anti-collision system.

Series completion: identify pattern in differences, squares, cubes, or alternating series. For letter series, note forward/backward jumps in alphabet positions.

Coding-decoding: letter shifting (e.g., +1, +2), reversal, substitution. Use position numbers A=1, B=2, ..., Z=26.

Blood relations: draw a family tree; use symbols for male/female and relationships. 'Brother of my father' = uncle; 'son of my mother' = brother or self.

Direction sense: use a rough diagram with N, S, E, W; net displacement is found using Pythagoras if turns are at right angles.

Syllogism: use Venn diagrams; 'All A are B' means A is a subset of B; 'Some A are B' means intersection is non-empty; conclusions must hold in all possible diagrams.

Non-verbal reasoning: mirror image (left-right reversal), water image (top-bottom reversal), paper folding, embedded figures, counting figures.

Seating arrangement: linear (facing north/south) and circular (facing centre/outside); note left/right reversals when facing opposite directions.

Clocks and calendars: clock angle = |30H − 5.5M| degrees; odd days method for day of week. A leap year has 2 odd days; 100 years have 5 odd days.

Number system: divisibility rules for 2,3,4,5,6,8,9,11; LCM and HCF: product of two numbers = LCM × HCF.

Percentage: x% of y = (x/100)×y; successive percentage change: a + b + ab/100. Profit/loss: SP = CP(1 ± profit%/100).

Simple interest: SI = P×R×T/100; compound interest: CI = P[(1+R/100)^T − 1]. For half-yearly compounding, rate halves and time doubles.

Ratio and proportion: if a:b = c:d then ad = bc. Partnership: profit shares proportional to capital × time.

Time, speed, distance: distance = speed × time; relative speed when moving in opposite directions = sum of speeds; same direction = difference. Train crossing a pole: time = length/speed.

Average: average = sum of quantities/number; weighted average. Mixture and alligation: (quantity of cheaper)/(quantity of dearer) = (dearer price − mean price)/(mean price − cheaper price).

Mensuration: area of circle = πr²; circumference = 2πr; volume of cylinder = πr²h; sphere volume = (4/3)πr³; surface area of sphere = 4πr².

Algebra: (a+b)² = a² + 2ab + b²; (a−b)² = a² − 2ab + b²; a² − b² = (a+b)(a−b). Quadratic roots: x = [−b ± √(b²−4ac)]/(2a).

Basic physics: Newton's laws, work = force × distance, power = work/time, energy conservation. SI units: force in newton, energy in joule, power in watt.

Chemistry: atomic number = number of protons; isotopes have same protons, different neutrons. pH < 7 acidic, > 7 basic; common salts and their uses.

Biology: cell is the basic unit; photosynthesis converts CO₂ and water to glucose and O₂ in presence of chlorophyll and sunlight; human body systems basics.

Environment: greenhouse gases (CO₂, CH₄, N₂O, CFCs); ozone layer depletion by CFCs; pollution types (air, water, soil, noise); renewable vs non-renewable energy sources.

Road safety: wear helmets and seat belts; follow traffic signals (red stop, yellow wait, green go); keep left; do not use mobile while driving; pedestrian crossing rules; railway level crossing precautions.

Indian Railways electrification: 25 kV, 50 Hz single-phase AC overhead system; return through rails. Traction substations feed OHE via catenary and contact wire.

Electric locomotive: DC series traction motors (or three-phase induction motors in modern locos) fed through transformer and rectifier/inverter. Pantograph collects current from OHE.

Signalling: track circuits detect presence of train; interlocking ensures safe routes; Kavach is an indigenously developed automatic train protection (ATP) system.

Railway electrical safety: use of protective relays, earth fault protection, and circuit breakers; maintenance of battery, lighting, and air-conditioning in coaches.

Electrical engineering practice: IS standards for wiring, earthing (pipe earthing, plate earthing), MCB and ELCB protection, cable colour code (red/yellow/blue for phases, black for neutral, green for earth).