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Complex Impedance in Phasor Notation The Kirchhoff Laws of Phasor Form (KCL) : (KVL) : Ohm’s Law Voltage-Divider Zeq =Z1+Z2 Equivalent Impedance Z1 Z2 + – + + – – Z + – Complex Impedances in Series Z + – Z1 Z2 + – Current-Divider Equivalent Impedance Complex Impedances in Parallel AC POWER ANALYSIS Instantaneous & Average Power Max. Average Power Transfer RMS Value & Apparent Power Complex Power & Power Factor Correction Instantaneous Power Instantaneous power (in watts) : the power at any instant of time Where: Instantaneous Power The instantaneous power p(t) entering a circuit Average Power Average Power (in watts) : the average of the instantaneous power over one period Where: Average Power Circuit Elements In purely resistive circuit, v and i are in phase. ?v = ?i. Therefore ? = 0. (a) Resistors: The average power is only dissipated in a purely resistive circuit. For a purely inductive and capacitive, the average power is zero. Circuit Elements In purely inductive circuit, v leads by 90o, therefore ? = 90o (b) Inductors: (c) Capacitors: In purely capacitive circuit, I leads by 90o, therefore ? = – 90o Effective or RMS Value The effective value of a periodic current is the dc current that delivers the same average power to a resistor as the periodic current. Finding the effective current: a) ac circuit b) dc circuit Effective or RMS Value The effective value of a periodic signals is its root mean square (rms) value. For any perodic function x(t) in general, the rms value is given by: Effective or RMS Value Effective or RMS Value The average power absorbed by resistor R can be written as: The average power can be written as: Apparent Power The apparent power (in VA) is the product of the rms value of voltage and current. S is known as the apparent power. Power Factor The power factor is the cosine of the phase difference between voltage and current. It is also the cosine of the angle of the load impedance. Power Factor : …