that is a good for me

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
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