ELECTRIC CIRCUITS EIGHTH EDITION JAMES W. NILSSON & SUSAN A. RIEDEL

CHAPTER 10 SINUSOIDAL STEADY – STATE POWER CALCULATIONS © 2008 Pearson Education

CONTENTS 10.1 Instantaneous Power 10.2 Average and Reactive Power 10.3 The rms Value and Power Calculations 10.4 Complex Power 10.5 Power Calculations 10.6 Maximum Power Transfer © 2008 Pearson Education

10.1 Instantaneous Power   Instantaneous power is the product of the instantaneous terminal voltage and current, or © 2008 Pearson Education The black box representation of a circuit used for calculating power

  The positive sign is used when the reference direction for the current is from the positive to the negative reference polarity of the voltage.   The frequency of the instantaneous power is twice the frequency of the voltage (or current). © 2008 Pearson Education 10.1 Instantaneous Power

Instantaneous power, voltage, and current versus ωt for steady-state sinusoidal operation © 2008 Pearson Education 10.1 Instantaneous Power

10.2 Average and Reactive Power Average Power   Average power is the average value of the instantaneous power over one period.   It is the power converted from electric to non-electric form and vice versa. © 2008 Pearson Education

10.2 Average and Reactive Power   This conversion is the reason that average power is also referred to as real power.   Average power, with the passive sign convention, is expressed as © 2008 Pearson Education

Reactive Power   Reactive power is the electric power exchanged between the magnetic field of an inductor and the source that drives it or between the electric field of a capacitor and the source that drives it. © 2008 Pearson Education 10.2 Average and Reactive Power

© 2008 Pearson Education 10.2 Average and Reactive Power Reactive Power  Reactive power is never converted to nonelectric power. Reactive power, with the passive sign convention, is expressed as

© 2008 Pearson Education 10.2 Average and Reactive Power Instantaneous real power and average power for a purely resistive circuit

Instantaneous real power, average power, and reactive power for a purely inductive circuit © 2008 Pearson Education 10.2 Average and Reactive Power

Instantaneous real power and average power for a purely capacitive circuit © 2008 Pearson Education 10.2 Average and Reactive Power

Power Factor Power factor is the cosine of the phase angle between the voltage and the current: © 2008 Pearson Education 10.2 Average and Reactive Power

The reactive factor is the sine of the phase angle between the voltage and the current: © 2008 Pearson Education 10.2 Average and Reactive Power

10.3 The rms Value and Power Calculations A sinusoidal voltage applied to the terminals of a resistor Average power delivered to the resistor © 2008 Pearson Education

The average power delivered to R is simply the rms value of the voltage squared divided by R. If the resistor is carrying a sinusoidal current, the average power delivered to the resistor is: © 2008 Pearson Education 10.3 The rms Value and Power Calculations

10.4 Complex Power   Complex power is the complex sum of real power and reactive power. A power triangle © 2008 Pearson Education | S | = apparent power P = average power Q = reactive power θ

10.4 Complex Power Three power quantities and their units © 2008 Pearson Education QuantityUnits Complex powervolt-amps Average powerwatts Reactive powervar

 Apparent Power is the magnitude of complex power. © 2008 Pearson Education 10.4 Complex Power

10.5 Power Calculations © 2008 Pearson Education The phasor voltage and current associated with a pair of terminals

10.6 Maximum Power Transfer A circuit describing maximum power transfer © 2008 Pearson Education

10.6 Maximum Power Transfer The circuit with the network replaced by its Thévenin equivalent Condition for maximum average power transfer © 2008 Pearson Education

10.6 Maximum Power Transfer Example: Determining Maximum Power Transfer without Load Restrictions. a)For the circuit shown below, determine the impedance Z L that results in maximum average power transferred to Z L. b)What is the maximum average power transferred to the load impedance determined in (a)? © 2008 Pearson Education

THE END