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Cheatsheet: Basic Electrical Technology
1. DC Circuit Analysis
- Ohm's Law V = IR
- Power P = VI = I²R = V²/R
- Series R: Req = R₁ + R₂ + ... + Rₙ → same current flows through all
- Parallel R: 1/Req = 1/R₁ + 1/R₂ + ... + 1/Rₙ → same voltage across all
- KVL: ΣV = 0 around any closed loop
- KCL: ΣIin = ΣIout at any node
2. Network Theorems
- Superposition Theorem - responses from independent sources summed linearly
- Thévenin: Replace network with Vth in series with Rth
- Norton: Replace network with In in parallel with Rn
- Max Power Transfer: RL = Rth
- Pmax = Vth² / (4 Rth)
- Condition for max power: RL = Rth → efficiency = 50% at max power transfer
- Reciprocity Theorem valid when: Network is linear, bilateral, passive (no dependent sources)
3. AC Circuit Fundamentals
- Instantaneous voltage: v(t) = Vm sin(ωt)
- Angular frequency: ω = 2πf (rad/s)
- RMS Value: Vrms = Vm / √2
- Impedance: Z = R + jX (Ω)
- Inductive reactance: XL = ωL
- Capacitive reactance: XC = 1/(ωC)
- Pure inductor (lagging): I lags V by 90°
- Pure capacitor (leading): I leads V by 90°
4. AC Power Analysis
- Active Power: P = VI cosφ (W)
- Reactive Power: Q = VI sinφ (VAR)
- Apparent Power: S = VI (VA)
- Power Factor: PF = cosφ = P/S
- Power Triangle: S² = P² + Q²
- Lagging PF (inductive): φ > 0° ⟹ Q > 0
- Leading PF (capacitive): φ < 0° ⟹ Q < 0
- Unity PF (purely resistive): φ = 0° ⟹ PF = 1
5. Three-Phase Systems
- Star - line voltage: VL = √3 · Vph
- Star - line current: IL = Iph
- Delta - line voltage: VL = Vph
- Delta - line current: IL = √3 · Iph
- 3-Phase Power: P = √3 · VL · IL · cosφ
- Balanced system condition: |VA| = |VB| = |VC|, phase shift = 120°
6. Magnetic Circuits
- MMF: ℱ = NI (Ampere-turns)
- Reluctance: ℛ = l / (μ₀ μᵣ A)
- Flux: Φ = ℱ / ℛ = NI / ℛ (Wb)
- Flux density: B = Φ / A (T)
- Field intensity: H = NI / l (A/m)
- Saturation region: B → Bsat as H → ∞ (non-linear beyond knee point)
7. Electromagnetic Induction
- Faraday's Law: e = -N · (dΦ/dt)
- RMS Induced EMF: E = 4.44 · f · N · Φm
- Self-inductance: L = NΦ / I = N²/ℛ (H)
- Mutual inductance: M = k √(L₁L₂), 0 ≤ k ≤ 1
- Lenz's Law: Induced EMF opposes the change in flux (hence the - sign)
8. Transformers
- Turns ratio: E₁/E₂ = N₁/N₂ = a
- Current ratio: I₁/I₂ = N₂/N₁ = 1/a
- Efficiency: η = Pout / Pin = 1 - (losses / Pin)
- Voltage Regulation: VR = (VNL - VFL) / VFL × 100%
- Max efficiency condition: Core loss Pi = Copper loss Pcu
- Good regulation: VR → 0% (small series impedance required)
9. DC Machines
- Back EMF: E = (P · Φ · Z · N) / (60 · A)
- Torque: T ∝ Φ · Ia
- Motor equation: V = E + Ia · Ra (motor)
- Generator equation: V = E - Ia · Ra (generator)
- Speed control (flux weakening): N ∝ E/Φ → if Φ ↓, N ↑ (above base speed)
- Speed control (voltage): N ∝ V → if V ↓, N ↓ (below base speed)
10. Induction Motors
- Synchronous speed: Ns = 120f / P (rpm)
- Slip: s = (Ns - Nr) / Ns
- Torque: T ∝ s · E² / (R₂² + (s · X₂)²)
- Normal operating range: 0 < s < 1 (motor mode)
- At no-load (ideal): s ≈ 0 (Nr → Ns)
- At standstill (start): s = 1 (Nr = 0)
- Slip at max torque: sm = R₂ / X₂
- Generator mode: s < 0 (Nr > Ns)
- Plugging (braking): s > 1
11. Synchronous Machines
- Synchronous speed: Ns = 120f / P (rpm)
- Power (salient): P = (EV / Xs) · sinδ
- Terminal voltage: V = E - Ia(Ra + jXs) (generator)
- Stability condition: Power angle δ < 90° (stable operation)
- Over-excited (leading PF supply): E > V → Ia leads V
- Under-excited (lagging PF supply): E < V → Ia lags V
12. Measuring Instruments
- PMMC - measures DC only; deflection ∝ I (linear scale)
- Moving Iron - measures AC & DC; deflection ∝ I² (non-linear scale)
- Dynamometer - measures AC & DC power; used in precision wattmeters
- Wattmeter - reads true average power P = VI cosφ
Ammeter shunt (Rₛₕ for PMMC): Rsh = Ig · Rg / (I - Ig) → Rsh ≪ Rg
Voltmeter series R: Rse = (V/Ig) - Rg → Rse ≫ Rg
13. Transients in Circuits
- RC charging: v(t) = V · (1 - e-t/RC)
- RC discharging: v(t) = V · e-t/RC
- RL build-up: i(t) = I · (1 - e-tR/L)
- RL decay: i(t) = I · e-tR/L
- RC time const: τ = RC (s)
- RL time const: τ = L/R (s)
- Steady state reached when: t ≥ 5τ (~99.3% of final value)
14. Resonance in AC Circuits
- Resonant frequency: fr = 1 / (2π√LC)
- Quality factor: Q = XL/R = ωrL/R = 1/(ωrCR)
- Bandwidth: BW = fr / Q = R / (2πL)
- Lower cutoff: f₁ = fr - BW/2
- Upper cutoff: f₂ = fr + BW/2
- At resonance (series RLC): XL = XC → Z = R (minimum)
- Series - current is: I = maximum (I = V/R)
- Parallel - impedance is: Z = maximum (anti-resonance)
- Selectivity: higher Q means: BW ↓ (narrower, more selective)
15. Semiconductors and Diodes
- Diode equation: I = Is · (eV/(ηVT) - 1)
- Thermal voltage: VT = kT/q ≈ 26 mV at 300 K
- Forward bias (conducts): V > 0 (typically VF ≈ 0.7 V for Si)
- Reverse bias (blocks): V < 0 and |V| < |VBR|
- Zener operates when: |VR| ≥ VZ (voltage regulation region)
- Ideal factor η: 1 ≤ η ≤ 2 (η=1 diffusion, η=2 recombination)
PN Junction - fundamental diode structure; depletion layer formed at junction
Zener Diode - operates in reverse breakdown; used for voltage regulation
Half-wave Rectifier - η ≈ 40.6%, ripple factor = 1.21
Full-wave Rectifier - η ≈ 81.2%, ripple factor = 0.48
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FAQs on Cheatsheet: Basic Electrical Technology
| 1. What are the key principles of DC circuit analysis? |  |
Ans. DC circuit analysis is based on Ohm's Law, which states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. The main techniques include Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL), which help in analysing complex circuits by applying conservation principles. KVL states that the sum of the electrical potential differences (voltage) around any closed network is zero, while KCL states that the total current entering a junction must equal the total current leaving the junction.
| 2. How do network theorems simplify circuit analysis? | |
Ans. Network theorems such as Thevenin's and Norton's theorems simplify complex circuits into simpler equivalent circuits. Thevenin's theorem allows a circuit to be represented by a single voltage source in series with a resistance, while Norton's theorem represents it as a current source in parallel with a resistance. These theorems facilitate easier analysis and calculations by reducing the number of components and focusing only on the essential elements affecting the particular circuit operation.
| 3. What is the significance of AC power analysis in electrical engineering? | |
Ans. AC power analysis is vital for understanding how alternating current systems operate, particularly how power is consumed and transmitted. It encompasses real power (measured in watts), reactive power (measured in reactive volt-amperes), and apparent power (measured in volt-amperes), with power factor playing a crucial role in efficiency. This analysis helps engineers design systems that optimise power usage and minimise losses in both residential and industrial applications.
| 4. What are the main types of three-phase systems and their applications? | |
Ans. The main types of three-phase systems are star (Y) and delta (Δ) configurations. In a star configuration, one end of each winding is connected to a common point, while the other ends are connected to the supply. It is used in applications requiring lower voltage and higher starting torque, such as motors. The delta configuration connects all windings in a loop, facilitating higher voltage and is often used in heavy machinery and industrial applications. Three-phase systems are preferred for their efficiency in power distribution and reduced conductor size compared to single-phase systems.
| 5. How do transformers work and what are their applications? | |
Ans. Transformers operate on the principle of electromagnetic induction, where a changing current in the primary coil creates a changing magnetic field that induces a voltage in the secondary coil. This allows for voltage transformation, either stepping up or stepping down the voltage level while conserving power. Transformers are widely used in power transmission and distribution systems, enabling efficient long-distance electricity transfer by reducing energy losses associated with high currents. They are also essential in various applications including electrical isolation and impedance matching in circuits.
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