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| Quantity | Symbol | Unit | Instrument | |---|---|---|---| | Current | I | Ampere (A) | Ammeter (series) | | Voltage | V | Volt (V) | Voltmeter (parallel) | | Resistance | R | Ohm (Ω) | Ohmmeter | | Power | P | Watt (W) | Wattmeter | | Energy | E | Joule (J) or kWh | Energy meter | | Frequency | f | Hertz (Hz) | Frequency meter |
Ohm's Law: V = IR Power: P = VI = I²R = V²/R Energy: E = Pt (kWh = kW × hours)
Series Circuit:
Parallel Circuit:
Kirchhoff's Laws:
AC Waveform: v = Vₘ sin(ωt + φ)
RMS Values: V_rms = Vₘ/√2 ≈ 0.707 Vₘ For 230V supply: Vₘ = 230×√2 ≈ 325V
Impedance Components:
| Component | Opposition | Phase Angle | Formula | |---|---|---|---| | Resistor (R) | Resistance | 0° (V and I in phase) | V = IR | | Inductor (L) | Reactance XL | +90° (V leads I) | XL = 2πfL | | Capacitor (C) | Reactance XC | -90° (I leads V) | XC = 1/2πfC |
Series RLC Circuit:
Power in AC:
A transformer transfers electrical energy between circuits through electromagnetic induction at the same frequency.
Working Principle: Faraday's law — changing flux in primary induces EMF in secondary.
Transformer Equation: E₁/E₂ = N₁/N₂ = I₂/I₁ = K (turns ratio)
Types:
Losses in Transformer:
Efficiency: η = Output/Input = Output/(Output + Losses) × 100% Maximum efficiency when copper loss = iron loss.
Converts mechanical energy to electrical energy. EMF equation: E = (PΦNZ)/(60A)
Types:
Converts electrical energy to mechanical energy. Back EMF: Eb = V - IaRa (opposes applied voltage) Speed: N = (V - IaRa)/(KΦ) — varies with field flux
Motor Starter: Used to limit starting current (5-6× rated) using resistance.
Why Three-Phase?
Star (Y) Connection:
Delta (Δ) Connection:
Three-phase power: P = √3 × VL × IL × cosφ
Wiring Systems:
Circuit Protection Devices:
| Device | Purpose | How it Works | |---|---|---| | Fuse | Overcurrent protection | Wire melts when current exceeds rating | | MCB (Miniature Circuit Breaker) | Overcurrent + short circuit | Magnetic + thermal trip | | ELCB/RCCB | Earth leakage protection | Detects current imbalance > 30mA | | Surge Protector | Voltage spike protection | MOV absorbs excess voltage |
Earthing: Connecting non-current-carrying metal parts to ground. Purpose: Safety (prevents electric shock), allows fault current to flow.
Q1: A 1kVA, 200/100V transformer is at 80% efficiency at full load with PF=0.8. Find input? Output = 1000 × 0.8 = 800W Input = Output/efficiency = 800/0.8 = 1000W
Q2: Find capacitance to give unity power factor to a 10kW motor with PF=0.8 lag on 230V, 50Hz supply. I = P/(V×PF) = 10000/(230×0.8) = 54.35A Q = P×tanφ = 10000×0.75 = 7500 VAR C = Q/(2πfV²) = 7500/(2π×50×230²) = 450 μF
Q3: Calculate line current in balanced 3-phase star load: 400V, 10Ω/phase, PF=1. Vph = 400/√3 = 231V; Iph = Vph/R = 231/10 = 23.1A = IL
Complete Electrical Engineering notes for Diploma — DC circuits, AC circuits, transformers, electrical machines, protection systems, and wiring with solved examples.
50 pages · 2.5 MB · Updated 2026-03-09
DC (Direct Current) flows in one direction with constant magnitude (batteries). AC (Alternating Current) periodically changes direction and magnitude (household supply, 50Hz in India).
AC can be easily stepped up/down using transformers. High voltage transmission reduces I²R losses. DC transmission has conversion losses and was historically harder to transform.
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