TSSPDCL Sub-Engineer cheat sheet

KCL: algebraic sum of currents at a node is zero; KVL: algebraic sum of voltages around any closed loop is zero - both hold for linear and nonlinear networks.

Thevenin equivalent: V_th = open-circuit voltage across the terminals; R_th = resistance seen with all independent sources killed (voltage sources shorted, current sources opened).

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

Superposition applies only to linear circuits and only to independent sources; it cannot be used for power because power is a nonlinear (I²R) quantity.

Series resonance: f_r = 1/(2π√(LC)); at resonance X_L = X_C, impedance is purely resistive, and Q = (1/R)√(L/C) = f_r/BW.

Three-phase star: V_L = √3 V_ph and I_L = I_ph; delta: I_L = √3 I_ph and V_L = V_ph; balanced three-phase power P = √3 V_L I_L cos φ.

Two-wattmeter method: total power P = W1 + W2; power factor angle φ = tan⁻¹[√3(W1 − W2)/(W1 + W2)].

Maximum power transfer occurs when R_L = R_th, giving efficiency of 50% for a resistive source; the theorem maximizes power, not efficiency.

First-order transient: voltage or current follows e^(−t/τ) with τ = RC for capacitive circuits and τ = L/R for inductive circuits; after 5τ the change is essentially complete.

Transformer EMF equation: E = 4.44 f N Φ_max; for a given frequency and flux, volts per turn is the same on both windings.

Ideal transformer: V1/V2 = N1/N2 = I2/I1; for a real transformer, copper loss = I²R and core loss is constant at rated voltage and frequency.

Open-circuit (no-load) test gives core (iron) loss and magnetizing branch parameters; short-circuit test gives full-load copper loss and series parameters.

Maximum efficiency occurs when copper loss equals iron loss, i.e. load fraction x = √(P_iron/P_copper, full load); all-day efficiency weights losses over 24 h.

DC machine EMF: E = (PΦNZ)/(60A); torque T = 0.159 PΦ I_a Z/A (N·m). Shunt motor has nearly constant speed; series motor must never be started unloaded.

DC motor speed control: N ∝ (V − I_a R_a)/Φ, so speed falls with load in a shunt motor and is controlled by armature voltage or field flux (Ward-Leonard).

Synchronous machine: N_s = 120f/P; EMF per phase E = 4.44 f Φ T_ph k_w, where k_w is the winding factor; excitation controls reactive power, not real power.

Induction motor slip s = (N_s − N_r)/N_s; rotor frequency = s·f; torque is maximum at s = R2/X2, and starting torque is developed only because the rotor circuit is closed.

Induction motor starting: direct-on-line suits small motors; star-delta reduces phase voltage to 1/√3 and starting torque to one-third; a slip-ring motor uses external rotor resistance to raise starting torque.

Load factor = average load / maximum demand; diversity factor = sum of individual maximum demands / maximum demand on the station; both are dimensionless and ≥ 1 for diversity.

Thermal plant heat rate = heat input / electrical output (kcal/kWh); overall efficiency = 860/heat rate in kcal per kWh (since 1 kWh = 860 kcal).

Transmission line surge impedance Z_c = √(L/C); surge impedance loading SIL = V_L²/Z_c; a line delivers natural power at unity power factor when terminated in Z_c.

Short line: V_s = V_r + I Z; medium line uses nominal-π or nominal-T; long line uses ABCD (generalized circuit) constants with hyperbolic functions.

Ferranti effect: receiving-end voltage exceeds sending-end voltage on a lightly loaded or open-circuit line because of charging current; compensated by shunt reactors.

Per-unit: Z_pu = Z_actual/Z_base, with Z_base = V_base²/S_base; per-unit impedance is the same on either side of a transformer when bases are chosen by turns ratio.

Symmetrical components: positive, negative and zero sequence; zero-sequence currents flow only through paths with a neutral return, so a delta winding blocks them.

Protection: overcurrent relay for overloads, distance (mho) relay for transmission lines, differential relay for transformers and busbars, Merz-Price circulating-current principle for generators.

Distribution: radial, ring-main and interconnected systems; a ring main improves reliability and voltage regulation; feeders are designed on current-carrying capacity while distributors are designed on voltage drop.

SCR: turns on when anode-cathode voltage exceeds forward breakover with gate signal; turns off only when anode current falls below holding current; latching current is the turn-on minimum.

Single-phase full-controlled bridge with resistive load: V_dc = (2V_m/π)cos α; with a highly inductive load the same expression holds and the converter can invert for α > 90° when a load EMF exists.

Three-phase fully controlled converter: V_dc = (3√3 V_m/π)cos α = 1.35 V_L cos α.

Buck chopper: V_o = D·V_s; boost: V_o = V_s/(1 − D); buck-boost: V_o = −V_s·D/(1 − D), where D is duty cycle.

Single-phase bridge inverter output is a square wave; PWM control shifts harmonics to higher frequencies, and the fundamental RMS of a unipolar/bipolar scheme depends on modulation index.

Cycloconverter converts fixed AC frequency to a variable lower AC frequency directly using phase-controlled thyristors; a matrix converter does the same with bidirectional switches.

DC drives: a phase-controlled converter feeding the armature gives variable armature voltage and hence variable speed; field weakening raises speed above base speed at constant power.

V/f control of an induction motor keeps air-gap flux constant; below base speed the drive is constant-torque, above base speed field weakening gives constant-power operation.

Commutation in thyristors can be natural (line) or forced (class A–F); class C and class D are common in inverters and choppers respectively.

PMMC instrument: deflection θ ∝ I, so it reads average value and is used for DC; a rectifier-type moving-coil meter reads average but is calibrated in RMS for sine waves.

Moving iron instrument: deflection θ ∝ I², reads RMS, works on AC and DC, and has lower accuracy than PMMC.

Ammeter shunt: R_sh = R_m/(m − 1); voltmeter multiplier: R_se = R_m(m − 1), where m is the multiplying factor.

Wattmeter error: the pressure-coil (voltage coil) current causes error; the compensating coil or the connection side (current coil on load side) reduces it.

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

Instrument transformer: CT secondary is rated 5 A or 1 A and must never be open-circuited; PT secondary is rated 110 V and must never be short-circuited.

Wheatstone bridge balances when P/Q = R/S; Maxwell bridge measures inductance, Schering bridge capacitance and loss angle, and Wien bridge frequency.

Control: transfer function = output/input with zero initial conditions; a second-order system has ζ and ω_n, with peak overshoot depending only on ζ and settling time ≈ 4/(ζω_n) for 2% band.

Routh-Hurwitz criterion: the number of sign changes in the first column equals the number of right-half-plane poles; a zero row is replaced by the derivative of the auxiliary polynomial.

Illumination laws: E = I/d² for a point source on a normal surface (inverse square); E = I cos θ/d² for an inclined surface; luminous efficacy is lumens per watt.

Lamp efficacy: incandescent about 10–15 lm/W, fluorescent about 50–80 lm/W, LED 80–150 lm/W, high-pressure sodium highest among discharge lamps.

Illumination design: number of lamps N = (E × A)/(Φ × UF × MF), where E is required lux, A area in m², Φ lumens per lamp, UF utilization factor, MF maintenance factor.

Electric heating: resistance heating uses I²R; induction heating suits surface hardening; dielectric heating suits insulators such as wood and plastics; arc heating reaches the highest temperatures.

Electric welding: resistance welding uses I²Rt at the joint; arc welding needs a drooping (falling) volt-ampere characteristic to stabilize the arc.

Traction: tractive effort F = 277.8 M_e α (N) for acceleration, and F = 98.1 W r (N) for train resistance; specific energy consumption is in Wh per tonne-km.

Traction motors: DC series motors suit traction because of high starting torque; AC single-phase series and three-phase induction motors are used with modern converters.

Refrigeration: 1 tonne of refrigeration = 3.5 kW (210 kJ/min); the coefficient of performance is the ratio of heat extracted to work input.

Electroplating: Faraday's laws give mass deposited m = ZIt; the current efficiency is the ratio of actual to theoretical deposit.

Diode: barrier potential about 0.7 V for silicon and 0.3 V for germanium; a Zener diode works in reverse breakdown as a voltage regulator.

Rectifiers: half-wave V_dc = V_m/π and ripple factor 1.21; full-wave V_dc = 2V_m/π and ripple factor 0.48; bridge needs four diodes.

BJT regions: cutoff (both junctions off), active (BE forward, CB reverse), saturation (both forward); β = I_C/I_B and α = β/(1 + β).

JFET/MOSFET: a MOSFET has very high input impedance; the transfer characteristic is I_D = I_DSS(1 − V_GS/V_P)² for a JFET.

Boolean algebra: De Morgan's laws (A+B)' = A'·B' and (AB)' = A' + B'; XOR gives 1 when inputs differ.

Karnaugh map: group 1, 2, 4, 8 adjacent cells; a group of 2ⁿ cells eliminates n variables; don't-care terms can be used to enlarge groups.

Flip-flops: SR, JK, D and T; JK toggles when J = K = 1; a D flip-flop is a transparent latch when clock is high and an edge-triggered register otherwise.

Counters: an n-bit ripple counter divides by 2ⁿ; a mod-N counter needs ⌈log2 N⌉ flip-flops; a ring counter has one flip-flop per state.

Number systems: binary-to-decimal by positional weights; 1's complement is bit inversion, 2's complement is inversion plus one; BCD uses 4 bits per decimal digit.

Earthing: plate or pipe earth electrode resistance should be low; the earth wire is connected to the equipment body, never to the neutral of the load; earth resistance is measured by the fall-of-potential method.

Protection devices: MCB trips on overload and short circuit; ELCB/RCCB trips on earth leakage current (typically 30 mA for personnel protection); fuse is a one-shot device.

Shock severity depends on current magnitude, path and duration; a current of about 50 mA through the body can be fatal; the body resistance falls when wet.

Indian Electricity Rules: a 3-pin socket has the earth pin longer and thicker; the earth pin is connected first and disconnected last; portable tools use a 3-core flexible cable.

Estimation: for domestic wiring, total load is computed from connected load and diversity; the main switch, distribution board and sub-circuit cable sizes are selected from current rating, not from voltage drop alone.

Cable size selection uses the formula for voltage drop V_d = (2·L·I·ρ)/A for a single-phase two-wire circuit, and three-phase drop is √3 times the per-phase drop.

Energy conservation: power factor improvement reduces line current and losses; capacitors are rated in kVAR, and kVAR = kW(tan φ1 − tan φ2).

Energy audit: preliminary (walk-through) audit identifies savings; detailed audit measures load profiles; the payback period is the capital cost divided by annual savings.

Tariff: two-part tariff has a fixed charge based on maximum demand plus an energy charge per kWh; a power-factor penalty or incentive applies when the power factor falls below a specified value.

Percentage and profit: profit% is on cost price unless stated; successive discounts of a% and b% equal a + b − ab/100 percent.

Simple interest I = PRT/100; compound amount A = P(1 + R/100)^T; for half-yearly compounding the rate is halved and periods doubled.

Time and work: if A does a job in x days and B in y days, together they take xy/(x + y) days; work done is proportional to time at constant rate.

Speed: distance = speed × time; for a train crossing a platform, total distance = train length + platform length; relative speed adds for opposite directions and subtracts for the same direction.

Averages and mixtures: alligation gives the ratio of two mixtures as the difference of their values from the mean; weighted average = Σwx/Σw.

Reasoning: in a series, check differences, then ratios, then alternating patterns; in coding-decoding, map the alphabet positions and check for reversal or shift rules.

Blood relations and directions: draw a diagram; for direction problems, use a coordinate sketch and apply Pythagoras for the shortest distance.

Syllogism: a conclusion follows only if it is true in every possible Venn diagram of the premises; 'some' statements are reversible, 'all' statements are not.

Static awareness: TSSPDCL is the Telangana State Southern Power Distribution Company Limited; India's installed capacity is dominated by thermal and renewable sources; units of power and energy are kW and kWh.

Subject-verb agreement: a singular subject takes a singular verb; with 'either...or' and 'neither...nor', the verb agrees with the nearer subject.

Articles: 'a' before consonant sounds, 'an' before vowel sounds (an hour, a university); 'the' for specific or unique references.

Prepositions: 'since' with a point of time, 'for' with a duration; 'between' for two, 'among' for more than two.

Common error types: wrong tense sequence, misplaced modifier, redundancy (return back), and wrong comparative (more better).

Computer basics: CPU has ALU and control unit; primary memory is RAM (volatile) and ROM (non-volatile); cache is faster than RAM and smaller.

Storage units: 1 byte = 8 bits; 1 KB = 1024 bytes; 1 MB = 1024 KB; 1 GB = 1024 MB; a nibble is 4 bits.

Operating system functions: process management, memory management, file system, and device drivers; Windows, Linux and macOS are examples.

Networks: LAN is local, WAN is wide; IP address identifies a host; HTTP is the web protocol; email uses SMTP for sending and POP3/IMAP for receiving.

MS Office and shortcuts: Ctrl+C copy, Ctrl+V paste, Ctrl+Z undo, Ctrl+S save, F5 slideshow in PowerPoint; a spreadsheet formula begins with '='.