Tamil Nadu HSE First Year Basic Electrical Engineering cheat sheet

Charge Q is measured in coulombs (C); one coulomb equals the charge carried by 6.24 × 10^18 electrons.

Current I is the rate of charge flow, I = Q/t, in amperes (A); 1 A = 1 C/s.

Potential difference V is work per unit charge, V = W/Q, in volts (V); 1 V = 1 J/C.

Resistance R is measured in ohms (Ω); conductance G = 1/R is measured in siemens (S).

Power P is measured in watts (W); 1 W = 1 J/s = 1 V × 1 A.

Energy W is measured in joules (J); commercial energy is billed in kilowatt-hours, 1 kWh = 3.6 × 10^6 J.

SI prefixes: k = 10^3, M = 10^6, m = 10^-3, µ = 10^-6, n = 10^-9, p = 10^-12.

Multiples and submultiples are converted by moving the decimal three places per prefix step, e.g. 4.7 kΩ = 4700 Ω.

Ammeter connects in series with low resistance; voltmeter connects in parallel with high resistance.

Ohm's law: V = I × R, valid at constant temperature for metallic conductors.

Rearranged forms: I = V/R and R = V/I.

Series circuit: same current through all elements; total voltage is the sum of drops.

Parallel circuit: same voltage across all branches; total current is the sum of branch currents.

A linear V–I graph through the origin indicates constant resistance; slope equals R.

Resistance of a conductor rises with temperature for metals (positive temperature coefficient).

Ohm's law fails for non-linear devices such as diodes, thermistors and filament lamps at varying temperature.

Power forms derived from Ohm's law: P = VI = I²R = V²/R.

Resistance of a wire: R = ρL/A, where ρ is resistivity in Ω·m, L length in m, A area in m².

Resistivity is a material property; doubling length doubles R, doubling area halves R.

Series: R_total = R1 + R2 + R3 + …; current is common, voltage divides in ratio of resistances.

Parallel: 1/R_total = 1/R1 + 1/R2 + …; two resistors give R_total = R1R2/(R1 + R2).

Equal resistors: n in series give nR; n in parallel give R/n.

Current divider: I1 = I_total × R2/(R1 + R2) for two parallel branches.

Voltage divider: V1 = V_total × R1/(R1 + R2) for two series resistors.

Resistor colour code: black 0, brown 1, red 2, orange 3, yellow 4, green 5, blue 6, violet 7, grey 8, white 9; gold ±5%, silver ±10%.

A rheostat varies resistance in circuit; a potentiometer divides voltage across its full track.

Electrical power: P = VI = I²R = V²/R, in watts.

Energy: W = P × t; in joules when P is in watts and t in seconds.

Energy in kWh = (power in W × time in hours) / 1000.

One unit of electricity on a domestic bill equals 1 kWh.

Efficiency η = output power / input power × 100%.

Heating effect: heat H = I²Rt joules (Joule's law).

Cost of energy = units consumed × tariff per unit.

A 100 W lamp run for 10 hours consumes 1 kWh (one unit).

A current-carrying conductor produces a magnetic field around it; field direction follows the right-hand grip rule.

Straight conductor field strength B = µ0I/(2πd) at distance d in free space.

Magnetic flux Φ is measured in webers (Wb); flux density B = Φ/A in tesla (T) or Wb/m².

Magnetomotive force (mmf) = NI ampere-turns for a coil of N turns carrying I.

Reluctance S = l/(µ0µrA); magnetic Ohm's law: Φ = mmf/reluctance.

Force on a current-carrying conductor: F = BIl sinθ, direction by Fleming's left-hand rule.

Force between parallel conductors: attraction when currents flow in the same direction, repulsion when opposite.

Solenoid field: B = µ0µrNI/l; inserting an iron core increases flux greatly.

A ferromagnetic core concentrates flux; permeability µr is much greater than 1 for iron.

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

Lenz's law: induced emf opposes the change producing it (the minus sign in Faraday's law).

Fleming's right-hand rule gives direction of induced emf: thumb motion, first finger field, second finger current.

Self-induced emf e = −L di/dt; inductance L is measured in henries (H).

Mutual inductance M links flux of one coil into another; e2 = −M di1/dt.

Energy stored in an inductor: E = ½LI².

Induced emf in a rotating coil of N turns: e = NBAω sin ωt, peak value NBAω.

Eddy currents are reduced by laminating the core; they cause heating losses.

A transformer works on mutual induction and needs varying (AC) supply, not steady DC.

Generator emf: E = (ΦZN/60) × (P/A) for a lap or wave wound machine, where A = P for lap and A = 2 for wave.

Lap winding: A = P, parallel paths equal poles, suited to high current, low voltage.

Wave winding: A = 2, two parallel paths, suited to high voltage, low current.

Motor back emf: Eb = V − IaRa; armature current Ia = (V − Eb)/Ra.

Torque: T = 0.159 ΦZIa(P/A) N·m, or T ∝ ΦIa.

Shunt motor has high starting torque and nearly constant speed; series motor must never run unloaded.

A starter limits starting current, since at start Eb = 0 and Ia = V/Ra is large.

Generator rule uses Fleming's right hand; motor rule uses Fleming's left hand.

Commutator converts AC in the armature to DC at the terminals in a DC generator.

RMS value = peak/√2 = 0.707 × peak; average value of half sine = 0.637 × peak.

Form factor = RMS/average = 1.11; peak factor = peak/RMS = 1.414 for a sine wave.

Frequency f = 1/T; angular frequency ω = 2πf.

Inductive reactance XL = 2πfL; capacitive reactance XC = 1/(2πfC).

Impedance Z = √(R² + (XL − XC)²); current I = V/Z.

Power factor = cos φ = R/Z; true power P = VI cos φ; reactive power Q = VI sin φ in VAR.

In a purely inductive circuit current lags voltage by 90°; in a purely capacitive circuit current leads by 90°.

Series resonance occurs at f = 1/(2π√(LC)); at resonance Z = R and current is maximum.

Single-phase power P = VI cos φ; apparent power S = VI in volt-amperes.

Live wire is red/brown, neutral is black/blue, earth is green or green-yellow.

Earth wire connects metal enclosures to earth and protects against shock from insulation failure.

Fuse rating is chosen slightly above normal full-load current; it protects against overload and short circuit.

MCB trips on overload and short circuit and can be reset; a fuse must be replaced.

Lighting circuits use 5 A rating; power circuits use 15 A or 16 A sockets.

Two-way switch wiring lets one lamp be controlled from two positions.

Wire gauge: lower gauge number means thicker wire and higher current capacity.

Conduit, casing-and-capping and cleat wiring are common domestic wiring systems; conduit gives the best protection.

Insulation resistance is measured with a megger, typically requiring at least 1 MΩ for a domestic installation.

Always switch off and isolate the supply before working on a circuit; treat live conductors as dangerous.

Current is measured by an ammeter in series; voltage by a voltmeter in parallel.

An ideal ammeter has zero resistance; an ideal voltmeter has infinite resistance.

A multimeter combines voltmeter, ammeter and ohmmeter functions; select the correct range and function first.

The megger (insulation tester) measures insulation resistance in megohms and is used on de-energized circuits.

The energy meter (kWh meter) measures electrical energy consumed over time.

An earth tester measures earth electrode resistance; a CRO displays waveform and amplitude.

Electric shock severity depends on current magnitude, path through the body and duration; 30 mA can be dangerous.

First aid for electric shock: isolate supply, do not touch the victim until isolated, then give artificial respiration if needed.

Verify Ohm's law by varying V and recording I; plot V against I and take the slope as R.

Measure resistance by voltmeter–ammeter method: R = V/I, with ammeter in series and voltmeter across the resistor.

Use a Wheatstone bridge or meter bridge for accurate resistance measurement; balance condition P/Q = R/S.

Verify series and parallel laws by measuring equivalent resistance with a multimeter and comparing with calculation.

Measure power in a single-phase circuit using a wattmeter; P = VI cos φ for a resistive load.

Calibrate an energy meter by counting disc revolutions for a known load and time.

Check continuity with a multimeter in ohmmeter mode on a de-energized circuit.

Record readings in a table, take repeated readings, and compute percentage error against calculated values.

When wiring a lamp and switch, connect the switch in the live conductor, never in the neutral.