Electrical Engineering Module 4 Quiz

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Module 4

• Covers three-phase networks and resonance, complex power in sinusoidal steady state, steady-state analysis of three-phase three-wire and four-wire unbalanced Y circuits.
• Includes unbalanced delta circuit, neutral shift, resonance in series and parallel RLC circuits, quality factor, bandwidth, impedance vs frequency for series resonant circuit.

Power in Sinusoidal Steady State

• Sinusoidal voltage (V= Vm Sin wt) applied across impedance (z=R+jX) establishes current (I= Im sin(wt-φ)).
• Power delivered (P(t)) at time t is calculated using the product of voltage and current.
• Average power (Pavg) is the net power flow over a cycle, calculated using VI cosφ.

Real Power

• The net or average power (Pavg) entering a load during one period is the real power.
• Pavg = VI cosφ, where 'φ' is the phase difference between voltage and current.
• Pavg differs depending on the type of load (resistive, purely reactive or combination).

Reactive Power

• If a passive network has inductors and/or capacitors, energy is stored and returned during each cycle.
• Reactive power (Q) is the power involved in this energy exchange.
• Q = VI sinφ (volt amperes reactive, VAR).

Complex Power, Apparent Power, and Power Triangle

• Complex power (S) combines real (P) and reactive (Q) powers as S = P + jQ.
• Apparent Power (|S|) = VI, expressed in volt-amperes (VA).
• The three quantities (S, P and Q) can be graphically represented on a right-angled triangle (Power Triangle).

Complex Power

• Complex Power (S) is defined by S = VI*.
• Real Power (P) = Re(S) = VI cosφ
• Reactive Power (Q) = Im(S) = VI sinφ
• Apparent Power (|S|) = |VI|
• A useful formula for determining complex power is S = VI* .

Balanced Three-Phase System

• Includes Delta and Star connected load analysis
• Phase voltages and currents are related by angle differences.
• Current in three lines should add to zero at all times in a balanced 3-wire system.
• In a 4-wire system, the addition of outgoing currents should be equal to the return current in the neutral wire.

Unbalanced Three-Phase Circuits

• Includes unbalanced Delta connected load.
• Source voltages are considered balanced
• Phase currents & impedances could be different from one another Unbalanced delta connected load

Millman's Theorem

• Provides a method to determine the currents and voltages across load impedances.
• Requires calculating the equivalent admittance for the parallel connected branches.

Series RLC Circuit and Resonance

• Impedance (z) of a series RLC circuit is calculated as z=R+j(XL-Xc).
• XL and XC are determined by frequency (f), inductance (L), and capacitance (C).
• Xc and XL inversely change as frequency is increased
• XL > Xc at high frequencies.
• Resonance occurs when XL = XC; at this point Z=R and voltage and current are in phase; this frequency (fo) is resonant frequency
• Q-factor (Q) is the ratio of voltage across inductor or capacitor to the supply voltage. Maximum energy storage to energy dissipation ratio at resonant frequency.
• Bandwidth (BW) is the range of frequencies for which the current or output voltage equals 70.7% of its resonant value at this frequency.
• Resonant frequency is found using the formula Wo = 1/(LC)

Parallel Resonance

• For a parallel RLC circuit, the impedance is calculated as the reciprocal of the sum of the reciprocals of each branch
• In parallel resonance, the impedance becomes very high, resulting in a low current.
• The condition for parallel resonance is defined by a relation between the ω values (ω₀) of the circuit elements

Test your knowledge on three-phase networks, resonance, and complex power in sinusoidal steady state with this quiz based on Module 4 of KTU Notes. Explore topics like unbalanced Y circuits, impedance, and real power calculations. Perfect for students wanting to solidify their understanding of electrical engineering principles.