1	Chapter 17 Power in AC Circuits
2	Active Power Instantaneous power to a load is p = v • i In an ac circuit p may be positive sometimes and negative other times Average value of the power, P Real power
3	Active Power Average value of instantaneous power, real power, active power, and average power mean the same thing
4	Reactive Power During times when p is negative, power is being returned from load This can happen for inductive or capacitive loads
5	Reactive Power Power that flows into these loads and back out is called the reactive power Average value of reactive power is zero
6	Power to a Resistive Load
7	Power to a Resistive Load p is always positive (except when zero) Power flows only from source to load Power is absorbed by the load Power to a pure resistance consists of active power only
8	Average Power Average value of power is halfway between zero and peak value of V_mI_m P = V_mI_m/2 If V and I are in RMS values Then P = VI
9	Average Power Also, P = I²R and P = V²/R Active power relationships for resistive circuits are the same for ac as for dc
10	Power to an Inductive Load Voltage and current of an inductor are 90°out of phase Average power to an inductance over a full cycle is zero There are no power losses associated with a pure inductance
11	Power to an Inductive Load Power that flows into and out of a pure inductance is reactive power only
12	Power to an Inductive Load p_L = VI sin 2wt (V and I rms values) Product VI is the reactive power, Q_L Q_L = VI = I²X_L = V²/X_L Units are VARs
13	Power to an Inductive Load VAR means Volt-Amperes-Reactive Inductive reactive power is represented as positive
14	Power to a Capacitive Load Voltage and current are 90°out of phase Average power over one complete cycle is equal to zero There are no power losses associated with a pure capacitance
15	Power to a Capacitive Load Power that flows into and out of a pure capacitance is reactive power only This power cycle is 180°out of phase with the inductive cycle
16	Power to a Capacitive Load p_C = –VI sin 2wt Q_C = VI Q_C = I²X_C = V²/X_C Capacitive reactive power is represented as negative Units are VARs
17	Power in More Complex Circuits It does not matter how a circuit or system is connected Sum of the power is found by summing individual powers Total real power P is found by summing each of the individual real powers
18	Power in More Complex Circuits Total Reactive power Q is found by summing individual Q’s Inductive powers are positive Capacitive powers are negative
19	Apparent Power Power to a load is VI If load has both resistance and reactance Product is neither the real power nor the reactive power, but a combination of both
20	Apparent Power This is called the apparent power, S S = VI = I²Z = V²/Z Units are volt-amperes (VA)
21	Relationship Between P,Q, and S P, Q, and S are related by the “power triangle”
22	Active and Reactive Power Equations P = VI cos q = S cos q Q = VI sin q = S sin q V and I are RMS values q is the phase angle between V and I Q is positive for inductive circuits and negative for capacitive circuits
23	Power Factor Ratio of real power to apparent power is called the power factor, F_p F_p = P/S = cos q Angle q is angle between voltage and current
24	Power Factor For pure resistance q = 0° For inductance, q = 90° For capacitance, q = -90° For a circuit containing a mixture, q is somewhere between 0° and ±90°
25	Power Factor Unity power factor For a purely resistive circuit, the power factor will be one For load containing resistance and inductance Power factor will be less than one and lagging Current lags the voltage
26	Power Factor For a circuit containing resistance and capacitance F_p is less than one and is leading
27	Why Equipment Is Rated in VA A highly reactive load May seem to require a small amount of power while requiring a large current Equipment is rated in VA to prevent overloading the circuit
28	Why Equipment Is Rated in VA Size of electrical apparatus required by a load Governed by its VA requirements
29	Power Factor Correction A load with a small power factor can draw a large current Can be alleviated by Cancelling some or all reactive components of power by adding reactance of opposite type to the circuit This is power factor correction
30	Power Factor Correction Industrial customers may pay a penalty for low power factors due to large currents required for highly reactive loads
31	AC Power Measurement To measure power in an ac circuit you need a wattmeter Meter consists of Current-sensing circuit Voltage-sensing circuit Multiplier circuit Averaging circuit
32	AC Power Measurement This will measure load voltage and current and find the product and the angle between these
33	Effective Resistance At high frequencies Resistance of a circuit may change R_eff = P/I² Anything that affects P will affect resistance
34	Effective Resistance Changing magnetic fields may set up eddy currents in conductors These cause power losses that affect effective resistance
35	Effective Resistance Ferromagnetic materials Power losses due to hysteresis effects Magnetically induced voltages created by a changing magnetic field cause a non-uniform current called a skin effect Causes an increase in resistance Energy escapes due to radiation resistance