This document discusses electrical power, energy, and power factor. It defines key concepts like watts, voltage, current, resistance, reactive power, and apparent power. Power is the rate of doing work and is measured in watts. Energy is the capacity to do work and is measured in joules. Power in AC circuits involves real power, reactive power, and apparent power. The power factor is the ratio of real power to apparent power and indicates the efficiency of the circuit. Reactive power reduces efficiency while resistance results in a power factor of 1.

1. ELECTRICAL Circuits

2. Lecture 10
Energy and Power

3. 3
Resistors and power
• Resistance :
• Rated by amount of resistance
– Measured in ohms (Ω)
• Also rated by power
– Measured in watts (W)

4. 4

5. 5
Power
• Power (P) is the amount of energy consumed
per unit time.
• Energy is the capacity of a system to perform
work.
• Force does work when it results in movement.

6. Electrical Examples
• The greater the power rating of a light, the
more light energy it can produce each second.
• The greater the power rating of a heater, the
more heat energy it can produce

7. 7
More Examples
• The greater the power rating of a motor, the
more mechanical work it can do per second
• Power is related to energy
– Capacity to do work

8. 8
Power
• Power is the rate of doing work W
– Power =
• Power is measured in watts (W)
• Work and energy measured in joules (J)
• One watt J/S=
– One joule per second
t
W

9. Power in Electrical
Systems
• Opposite charges attract.
• Like charges repel.
• If we move a negative electron towards another
electron we perform work because we are
moving against an opposing force.
• Moving two electrons toward two other electrons
requires more work because there is more
opposing force.
• We often need a convenient way to describe how
much work is required to move charge from one
point to another. That concept is voltage.

10. • If moving a positive charge from point B to point
A requires positive work, then point A is said to
have a positive voltage with respect to B.
• The relationship between the work required in
joules, the amount of charge in coulombs, and
the voltage in volts is:
• Since W and Q can be positive or negative, it
stands to reason that V can be positive or
negative also.

11. Power in Electrical
Systems
• P= W/t
• From V = W/Q and I = Q/t, we get
• P = VI
• From Ohm’s Law, we can also find that
• P = I2R and P = V2/R
• Power is always in watts
11

12. 12
Power in Electrical Systems
• We should be able to use any of the power
equations to solve for V, I, or R if P is given
• For example:
2
2
I
P
P
V
PR
V
R
P
I




R

13. 13
Power Direction
Convention
If P has a positive value, power transfer is into the box
If P has a negative value, power transfer is out of the box

14. 14
Typical Power Ratings
Appliance Power Rating
Laptop computer 20~30 W
Radio 70 W
Washing machine 500 W
Microwave oven 1000 W
Heater 1300 W

15. Resistors
• Rated by amount of resistance
– Measured in ohms (Ω)
• Also rated by power
– Measured in watts (W)
15

16. 16
Energy
• Energy =
– Power × time
• Units are joules (Watt-seconds)
– Watt-hours
– kilowatt-hours

17. 17
Energy
• Energy use is measured in kilowatt-hours by
the power company
• For multiple loads
– Total energy is sum of the energy of individual
loads

18. 18
Energy
• To find the cost of running a 2000-watt heater
for 12 hours if electric energy costs RM0.08
per kilowatt-hour:
– Cost = 2kW × 12 hr × RM0.08 Cost = RM1.92

19. Law of Conservation of
Energy
• Energy can neither be created nor destroyed
– Converted from one form to another
• Examples:
– Electric energy into heat
– Mechanical energy into electric energy
19

20. Law of Conservation of
Energy
• Energy conversions
– Some energy may be dissipated as heat, giving
lower efficiency
20

21. Watt-hour Meters
• Energy is measured by watt-hour meters
• Electromechanical device that incorporates a
small motor whose speed is proportional to
power to the load
21

22. Watt-hour Meters
22

23. Power/energy in AC

24. Introduction
• Instantaneous power
– Time-varying power
– Denoted by p, or p(t) (small letter)

25. If in phase, Always positive.

26. But

27. ‘
a positive value for p means that power transfer is in the direction of
the reference arrow, while a negative value means that it is in the
opposite direction.

28. Power in ac
• Active Power
• Reactive Power
• Apparent Power

29. Active Power
• Average power to the load
– Denoted by the letter P
• If average power is positive:
– Power is dissipated by the load
• P is also called real power, or active power
– Average value of the instantaneous power.

30. Reactive Power
• Portion of the power that flows into the load
and then back out
– Average value is zero
• Reactive power does no useful work
• Extra current is required to create reactive
power
– Adds cost to the system

31. Apparent Power
• If a load contains both resistance and
reactance:
VI represents apparent power, S
• S = VI (volt-amperes)

32. Apparent Power
• For heavy power apparatus:
• Common to rate electrical apparatus in terms
of operating voltage and current

33. The Relationship
Between P,Q, and S
• Power triangle
– Relationship between P, Q, and S
We can also define the complex power S = P + jQ
** The apparent power is the magnitude of complex power .

34. Real and Reactive Power
Equations
V and I are RMS values
 is the phase angle between V and I
Q is positive for inductive circuits and negative for
capacitive circuits

35. Power Factor
• Ratio of real power to apparent power is
called the power factor, Fp
Fp =
𝑃
𝑆
=
𝑆 𝑐𝑜𝑠𝜃
𝑆
= cos 
 is angle between voltage and current

36. Power Factor
• For pure resistance  = 0º
• For inductance,  = 90º
• For capacitance,  = −90º
• For a circuit containing a mixture,  is
somewhere between 0º and 90º

37. Unity, Lagging, and
Leading Power Factor
• Unity power factor
– Power factor of one
– True for a purely resistive circuit
• For load containing resistance and inductance:
– Current lags the voltage
– Power factor described as lagging

38. Unity, Lagging, and
Leading Power Factor
• For a circuit containing resistance and
capacitance:
– Current leads voltage
– Power factor is described as leading

39. 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
• Size of electrical apparatus required by a load
– Governed by its VA requirements

40. 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

41. References
• Electricity and Electronics by Gerrish, Dugger and
Roberts, 10th edition, 2009, GW Publisher
• Circuit Analysis: Theory and Practice by A. H.
Robbins, W. C. Miller, 4th edition, 2006, Thomson
Delmar Learning
• Introductory Circuit Analysis by R. L. Boylestad, 11th
edition, 2007, Prentice Hall
41