1. Principles & Applications
Electricity
Principles & Applications
Sixth Edition
Richard J. Fowler
Chapter 9
Power in AC Circuits
© Glencoe/McGraw-Hill

2. INTRODUCTION Phase Shift True Power Apparent Power Angle Theta
Power Factor

3. Ac-Power Facts Resistance doesn’t cause phase shift.
Reactance causes 90° of phase shift.
Theta is the angle by which the current leads or lags the voltage.
Trigonometric functions can be used to find the resistive and reactive parts of a phasor.
Apparent power calculations ignore phase shift.
It is advantageous for a system to operate with a power factor close to one.

4. Power in a Resistive Ac Circuit
Note that both
power pulses
are positive.
There are only
two pulses per
cycle. Voltage
and current are
in-phase. 5V V
2 A I
P = IV in an ac circuit containing only resistance.
P =
2 A x x
5V x =
5 W

5. Resistive-Power Quiz Power equals current times voltage in an ac
circuit when the only load is ____.
resistance
Use ____ values of current and voltage when
calculating power.
rms
Without phase shift, there are ____ power
pulses for each cycle.
two
There are no ____ power pulses when current
and voltage are in phase.
negative
An ac circuit with a 30-VP-P source and a 10-W
resistor load uses ____ watts of power.
11.25

6. Reactance Causes Phase ShiftV I
50°
A combination circuit with capacitance causes I to lead V.

7. Reactance Causes Phase Shift
60° V I
A combination circuit with inductance causes V to lead I.

8. = Working with Right Triangles opposite adjacent tan q = opposite
hypotenuse
opposite
hypotenuse
opposite side
sin q = q
adjacent side
adjacent
hypotenuse
cos q =
Iresistive
Ireactive
Isource
Vsource q
Iresistive
Ireactive
Isource q =
The hypotenuse can be either the total voltage or the total current.
Of course, the sides must be the same quantity as the hypotenuse.

9. Combination-Loads Quiz
Capacitance causes current to ____ voltage.
lead
Inductance causes current to ____ voltage.
lag
The ____ of a triangle of current phasors
represents the total current.
hypotenuse
The resistive current is ____ amperes when
theta is 40° and the total current is 12 amperes.
9.2
The total voltage is ____ volts when theta is
25° and the reactive voltage is 40 volts.
94.6

10. Power in a Phase-Shifted Circuit
cos 30° = 0.866
30° 3V
2 A I V
The power pulse is negative when I and V have opposite signs.
P = I V cos q =
2 A x x
3V x x
0.866 =
2.6 W

11. Power in a Pure Reactance Circuit
The
negative
power
pulses
cancel
the
positive
pulses.
There is
no true
power. I V
90°
This circuit has capacitance because I leads V.

12. Two Types of Power in Ac CircuitsV
25 V
Combination of
resistance
and
reactance
or calculated
using the formula
Power (true power) is measured with a wattmeter
P = IV cos q.
Measured P = 80 W.
Apparent power is determined by measuring
current
and voltage
and then using the formula
Papp = IV.
Papp = 4 A x 25 V = 100 VA
When the load is all resistance, power (P) = apparent power (Papp).

13. Determining Power Factor (PF) & Angle Theta (q)V
30 V
Combination of
resistance
and
reactance
The measured power,
current,
and voltage
can be used to
determine power factor and angle theta.
Papp = 3 A x 30 V = 90 VA
PF = cos q = P / Papp = 75.5 W / 90 VA = 0.839
q = arccos = 33°
(Arccos means the angle that has this cos.)

14. Calculating Currents
Determine the resistive and reactive currents when the
source current is 43 A and the power factor is 0.92.
cos q = Iresistive / IT
Therefore, Iresistive = IT x cos q
Iresistive = 43 A x = A
arccos = 23.1°
( Arccos means the angle that has this cos.)
And, tan 23.1° =
tan q = Ireactive / Iresistive
Therefore, Ireactive = Iresistive x tan q
Ireactive = A x = A

15. Combination-Load-Power Quiz
There are ____ negative power pulses per cycle
when current and voltage are out of phase.
two
With combination loads, P = IV cos q will
yield the ____ power.
true
With combination loads, P = IV will
yield the ____ power.
apparent
The unit for apparent power is the _____. VA
The power is ____ watts when I = 16 A,
V = 240 V, and q = 20°.
3608.4
The power factor is ____ when P = 860 W,
I = 10 A, and V = 120 V.
0.717

16. REVIEW
Phase Shift
True Power
Apparent Power
Angle Theta
Power Factor