Vidyut Sahayak (Pareshan) Contractual cheat sheet

Ohm's law: V = IR; power P = VI = I²R = V²/R for resistive circuits.

Series: R_eq = R1 + R2 + ... and the same current flows. Parallel: 1/R_eq = 1/R1 + 1/R2 + ... and the same voltage appears across each branch.

KCL: sum of currents entering a node equals sum leaving. KVL: sum of voltage drops around a closed loop equals sum of source EMFs.

Thevenin equivalent: V_th = open-circuit voltage; R_th = resistance looking into terminals with independent voltage sources shorted and current sources opened.

Norton equivalent: I_N = short-circuit current; R_N = R_th; conversion I_N = V_th/R_th.

Superposition applies to linear circuits with multiple independent sources; it cannot be used for power because power is nonlinear.

Sinusoidal RMS = V_m/√2; average of a full sine = 0; form factor for sine = 1.11; peak factor = 1.414.

Series resonance: f_r = 1/(2π√(LC)); at resonance X_L = X_C, Z = R is minimum, current is maximum, and power factor is unity.

RC time constant τ = RC; RL time constant τ = L/R; after one τ a capacitor charges to 63.2% of final value.

Transformer EMF equation: E = 4.44 f N Φm; ideal voltage ratio V1/V2 = N1/N2; current ratio I1/I2 = N2/N1.

Transformer losses: copper loss varies as load current squared; iron loss is nearly constant; maximum efficiency occurs when copper loss equals iron loss.

DC generator EMF: E = (PΦNZ)/(60A); for lap winding A = P, for wave winding A = 2.

DC motor torque: T = 0.159 PΦIZ/A N·m; speed N ∝ (V − IaRa)/Φ.

Three-phase induction motor: Ns = 120f/P; slip s = (Ns − Nr)/Ns; rotor frequency f_r = s f.

Synchronous speed depends on supply frequency and pole pairs; a synchronous motor runs only at Ns and can supply or absorb reactive power by field excitation.

Star-delta starting reduces phase voltage to 1/√3 and starting torque to 1/3; DOL, autotransformer, and soft starters also limit starting current.

Transformer cooling codes include ONAN, ONAF, and OFAF; Buchholz relay protects oil-immersed transformers.

Three-phase power P = √3 V_L I_L cosφ; reactive power Q = √3 V_L I_L sinφ.

Short transmission line: V_s = V_r + I Z; regulation = (|V_s| − |V_r|)/|V_r| × 100%.

Surge impedance Z_c = √(L/C); surge impedance loading SIL = V_L²/Z_c.

Ferranti effect: receiving-end voltage rises above sending-end voltage on long unloaded or lightly loaded lines due to charging current.

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

Per unit: Z_pu = Z_actual/Z_base; I_base = S_base/(√3 V_base); per-unit transformer impedance is unchanged when base voltage follows the turns ratio.

Protection: overcurrent relay for overload and faults; distance relay for transmission-line zones; differential relay for transformer and generator protection.

Buchholz relay detects incipient transformer faults; earth fault relay detects leakage current to earth.

Load flow: slack bus has fixed V and δ; PV bus has fixed P and V; PQ bus has fixed P and Q.

Circuit breaker ratings include rated voltage, rated current, breaking capacity, making capacity, and short-circuit MVA.

SCR turns on with anode positive and a gate pulse; it turns off when anode current falls below holding current; the gate cannot turn it off.

Single-phase full-wave rectifier average output V_dc = 2V_m/π; three-phase full-wave average V_dc = 3√3 V_m/π.

Buck chopper V_o = D V_s; boost chopper V_o = V_s/(1 − D); duty cycle D = T_on/T.

Inverter converts DC to AC; PWM controls both output voltage and frequency; VSI uses a capacitive DC link and CSI uses an inductive DC link.

Induction motor V/f control keeps V/f constant to maintain air-gap flux; below base speed constant torque is available, above base speed field weakening applies.

Freewheeling diode provides a path for inductive current, protects switches, and improves input power factor.

IGBT has a MOSFET input and BJT output; it is used in medium and high power drives and has gate turn-off capability unlike an SCR.

Triac controls AC power in both half cycles; a diac is used for triggering; phase control varies RMS output voltage.

Four-quadrant drive operates in both directions of speed and torque, allowing forward motoring, forward braking, reverse motoring, and reverse braking.

PMMC measures average DC; moving iron measures RMS of AC or DC; electrodynamometer measures true RMS and works on AC and DC.

Wattmeter: current coil in series with the load, pressure coil across the supply; single-phase reading = V I cosφ.

CT secondary must never be opened under load; PT secondary must never be short-circuited.

Wheatstone bridge measures medium resistance; Kelvin double bridge measures low resistance; Megger measures insulation resistance.

Energy meter constant is revolutions per kWh; creeping is prevented by two diametrically opposite holes in the disc.

Error = (measured value − true value)/true value × 100%; accuracy, precision, and resolution are separate specifications.

Thermocouple and thermopile instruments measure RMS current and high-frequency signals; rectifier-type meters measure average and are calibrated in RMS for sine waves.

CRO measures voltage, time period, frequency, and phase; Lissajous figures give the frequency ratio of two signals.

Open-loop system has no feedback; closed-loop system has feedback, reduced sensitivity, and reduced steady-state error.

Transfer function = Laplace transform of output divided by Laplace transform of input, with zero initial conditions.

Second-order system: natural frequency ω_n and damping ratio ζ; percent overshoot = 100 e^(−ζπ/√(1−ζ²)).

Settling time ≈ 4/(ζω_n) for a 2% band; peak time = π/(ω_n√(1−ζ²)).

Routh-Hurwitz: number of sign changes in the first column of the Routh array equals number of right-half-plane poles.

Type 0 system has finite step error and infinite ramp error; Type 1 has zero step error and finite ramp error; Type 2 has zero ramp error.

Bode plot: gain margin is the negative of gain at phase crossover; phase margin is 180° plus phase at gain crossover.

PID: P reduces rise time, I eliminates steady-state error, D reduces overshoot and improves stability.

Left-half-plane poles give a stable response; right-half-plane poles give an unstable response.

Silicon diode forward drop ≈ 0.7 V; germanium ≈ 0.3 V; reverse saturation current roughly doubles for every 10°C rise.

BJT relations: β = I_C/I_B; α = I_C/I_E; β = α/(1 − α); I_E = I_B + I_C.

NAND and NOR are universal gates; XOR gives 1 when inputs differ; XNOR gives 1 when inputs are equal.

De Morgan: (A + B)′ = A′B′; (AB)′ = A′ + B′.

JK flip-flop toggles when J = K = 1; D flip-flop output follows D at the clock edge; SR flip-flop has an invalid state when both inputs are 1.

Half adder: sum = A ⊕ B, carry = AB; full adder includes carry-in.

Ideal op-amp: infinite input impedance, zero output impedance, infinite open-loop gain; virtual short at inputs with negative feedback.

Inverting amplifier gain = −R_f/R_in; non-inverting gain = 1 + R_f/R_in.

ADC resolution = V_ref/2^n; an n-bit converter has 2^n quantization levels.

Indian new wiring colours: brown phase, blue neutral, green-yellow earth; old colours: red phase, black neutral, green earth.

Lighting circuits use 1.5 mm² copper conductor; 2.5 mm² for socket outlets; 4 mm² or higher for power circuits.

Earth resistance should be low; IS 3043 gives the code of practice; earth resistance is measured by the fall-of-potential method.

MCB Type B trips at 3–5 times rated current, Type C at 5–10 times, Type D at 10–20 times.

RCCB with 30 mA sensitivity protects persons against earth leakage; it does not protect against overload or short circuit.

Conduit wiring uses draw boxes; limit bends between boxes; PVC conduit is flame retardant.

Electrical fire is Class C; use CO2 or dry powder extinguisher, never water.

First aid for electric shock: isolate supply, call help, check breathing, and start CPR if trained.

Insulation resistance of a low-voltage installation should be at least 1 MΩ.

Wind power available P = 0.5 ρ A v³; turbine output is multiplied by power coefficient Cp; Betz limit is 59.3%.

Solar cell fill factor = P_max/(V_oc I_sc); efficiency = P_max/(incident solar power).

PV modules in series add voltages; in parallel add currents; bypass diodes prevent hot spots.

MPPT algorithms include perturb and observe and incremental conductance; they adjust duty cycle for maximum power.

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

Power factor improvement reduces line current and losses; capacitor banks supply reactive power.

LED lamps have higher efficacy than CFL and incandescent lamps; electronic ballasts save energy.

Net metering allows rooftop solar consumers to export surplus energy to the grid.

Gujarat state animal: Asiatic lion; state bird: greater flamingo; state tree: banyan.

Sardar Sarovar Dam is on the Narmada River in Gujarat.

Gujarati is an Indo-Aryan language written left to right in an abugida script.

Reasoning topics include coding-decoding, number series, blood relations, direction sense, and syllogism.

Syllogism conclusions must follow from premises; Venn diagrams are used to test validity.

Coding-decoding: identify letter shifts or position patterns before applying the rule.

English grammar: subject-verb agreement, active and passive voice, and direct and indirect speech.

General awareness: Ohm's law, SI units, and electrical safety symbols.