UNIT 3

Ac Circuits, Resonance And Three-Phase Systems

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Sinusoidal signals and phasors, impedance and admittance in frequency domain, node and mesh analysis in phasor domain, power in AC circuits, average and reactive power, complex power, power factor and correction, resonance in series and parallel RLC circuits, balanced three-phase circuits, phase sequence, line and phase quantities, and power in three-phase loads.

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Sinusoidal Signals, Peak, RMS Values, and Phasor Representation

Sinusoidal waveforms, amplitude, angular frequency omega, phase angle, period and frequency, instantaneous, peak, average, and root-mean-square (RMS) values, form factor, peak factor, and phasor transformation via Euler's identity.

Important

Impedance and Admittance in Frequency Domain

Phasor V-I relationships for resistor (V = IR), inductor (V = j omega L I), and capacitor (V = I / j omega C), reactance (X_L, X_C), complex impedance (Z = R + jX), complex admittance (Y = G + jB), and impedance triangles.

Important

Nodal and Mesh Analysis in Phasor Domain

Application of Kirchhoff's laws (KCL and KVL) to AC circuits in phasor domain, formulation of node-voltage equations and mesh-current equations with complex impedances, and phasor diagrams.

Important

Power in AC Circuits: Average, Reactive, and Complex Power

Instantaneous AC power, active/real power (P = V_rms I_rms cos theta), reactive power (Q = V_rms I_rms sin theta), apparent power (S = V_rms I_rms), complex power (S = V_rms I_rms* = P + jQ), and the power triangle.

Important

Power Factor and Power Factor Correction

Definition of power factor (pf = cos theta = P/S), lagging vs leading power factor, technical and economic disadvantages of low power factor, sizing shunt capacitor banks for power factor improvement.

Important

Resonance in Series and Parallel RLC Circuits

Series resonance condition (X_L = X_C), resonant frequency (omega_0 = 1/sqrt(LC)), minimum impedance (Z_0 = R), voltage magnification across L and C, quality factor (Q = omega_0 L / R), bandwidth (BW = omega_0 / Q), and parallel RLC resonance.

Important

Balanced Three-Phase Circuits: Phase Sequence, Star and Delta Connections

Advantages of 3-phase systems, generation of balanced 3-phase voltages, phase sequence (RYB vs RBY), Star (Y) connection line vs phase quantities (V_L = sqrt(3) V_ph, I_L = I_ph), Delta (Delta) connection line vs phase quantities (I_L = sqrt(3) I_ph, V_L = V_ph), and role of neutral.

Important

Power in Three-Phase Loads and Two-Wattmeter Measurement

Power expressions in balanced 3-phase loads, two-wattmeter method for power measurement, derivation of total active power (W_1 + W_2 = P), power factor determination from wattmeter readings, and wattmeter responses under varying power factors.

Important