ee1 chapter6 power_energy&efficiency
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Apr 15, 2023
Lecturer Name lecturer_email@ite.edu.sg
Contact Number
IT2001PAEngineering Essentials (1/2)
Chapter 6 – Power, Energy and Efficiency
2
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Lesson Objectives
Upon completion of this topic, you should be able to: Calculate power and energy in electrical circuits..
3
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Specific Objectives
1. State the units for :
Quantity of electricity
Energy
Power
2. Establish the following equations :
Q = I x t
E = P x t
3. Establish the following equations of power
P = I2 x R = V2/R = V x I
4
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Specific Objectives
4. Solve simple problems involving a maximum of three resistors relating to :
Quantity of electricity
Electrical energy
Electrical power
5. Calculate energy consumption of an electrical load in kWh.
6. Calculate the cost of energy consumed by an electrical load for a given power and time.
7. Convert the unit from kWh to Joules and vice versa.
5
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Units
Unit of Voltage : Volts (v)
Unit of Current : Ampere (A)
Unit of Resistance : Ohms ()
Recall units
6
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Units
Unit of Charge: Coulomb (Q)
Unit of Energy : Joules (J)
Unit of Power : Watts or J/s (W)
7
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Alternative Unit for Energy
Energy (Joules, J) can also be expressed in kilowatt-hours (kWh).
1 kWh = 1000 Watt-hours
= 1000 x 3600 watt-seconds
= 3,600,000 Joules
= 3.6 MJ
Watt-seconds=Joules
8
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
What is Energy
Energy is ability or capacity for doing work.
Work cannot be done without energy being used.
Mechanical, electrical and heat energy are all measured in joules (J)
9
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Energy
Energy may exist in several forms and may be changed from one form to another.
A lead-acid cell changes chemical energy to electrical energy on discharge and vice-versa on charge.
A generator changes mechanical energy to electrical energy;
An electric radiator converts electrical energy to heat energy, and etc
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Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
What is Energy
When current passes through a resistance, the collisions of the electrons gives off heat, a form of energy.
heat produced by current through
resistance is energy loss
- +
VS
11
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
What is Energy
Heat energy produced in the resistor is proportional to :
a) square of the current - I2
b) resistance of the resistor - R
c) duration of time - t in seconds
Energy = I2Rt joules
= Power x Time
12
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Cost of Energy
The cost of electrical energy is calculated by multiplying the number of units of energy consumed in kWh and the cost per unit.
1 unit = 1 kWh
13
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-1 (Cost of Energy)
A colour television rated at 1600 W operates for 5 hours a day for 30 days.
(a) What is the total energy consumed?
(b) What is the monthly consumption cost if the cost per unit is 18 cents?
Solution :
(a) Energy = 1600 x 5 x 30 = 240 kWh
(b) cost = 240 x $ 0.18 = $ 43.2
14
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
What is Electrical Power? Power is the rate of doing work.
Power is measured by how fast energy is being used.
Power = work done in joules/time taken
in seconds
One watt of power is obtained when a current of one ampere passes through a potential difference of one volt.
Unit: J / s or watts
15
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
High power consumption
Low power consumption
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Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Equations of Power
As power is work done per sec therefore
P = IR2tt
P = I2R
Ohm’s law
I = V/ R
R = V/ I
P = VR
2R = V2
R
= I2 VI
= VI
17
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Total Power
The total power for both series and parallel circuits, is equal to the sum of the powers in each resistor :
PT = P1 + P2 + P3 + … … + Pn
18
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Comparison
SERIES PARALLEL
PT = P1 + P2 + P3 + … … + Pn
IT = I1 + I2 + I3 + … + In
VS = V1 = V2 = V3 = … = Vn
IT = I1 = I2 = I3 = … = In
RT = R1 + R2 + R3 + … + Rn
VS = V1 + V2 + V3 + … + Vn
1 1 1 1 1
RT R1 R2 R3 Rn
= + + … +
19
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Efficiency
The efficiency of an electric circuit is the ratio of output to the input expressed in percentage. It is symbolized by
Efficiency of electric circuit,
Output power is always smaller than input due to losses Efficiency is always < 100%
20
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Problem Solving
Power
Calculations
21
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-2 (Efficiency)
The output of a generator is 1500W and the input is equivalent to 1900W.
Calculate its percentage efficiency.
= (1500/1900)x100 = 78.9%
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Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-3
Calculate the total power consumed by the circuit below (i.e. the power dissipated in R).
Power dissipated in RV2
RP = = 180W=
602V2
20
Vs 60V
R=20 +
-R
23
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-3… cont”d
Power dissipated in RP = I2 x R = 32A x 20 = 180W
I = = = 3A V 60V R 20
Vs 60V
R20
24
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-4
Calculate the power dissipated in R1 , R2
and the total power consumed by the circuit below.
R1 = 10
VS = 60V
R2 = 20
+ -
25
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
R1 = 10
VS = 60V
R2 = 20
+ -
RT = R1 + R2 = 10 + 20 = 30
IT =VS
RT
= 2A= 60V 30
Example 6-4…….cont”d
26
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-4 ….cont”d R1 = 10
VS = 60V
R2 = 20
+ -
Power dissipated in R1
Power dissipated in R2
P1 = IT2 x R1 = 22A2 x 10 = 40W
P2 = IT2 x R2 = 22A2 x 20 = 80W
27
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-4….. Cont”d
R1 = 10
VS = 60V
R2 = 20
+ -
or PT = P1 + P2 = 40W + 80W = 120W
= 2A x 60V = 120WPT = IT x VS
Total power dissipated
28
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-5
Calculate the power dissipated in R1 , R2 and the total power consumed by the circuit below.
R1
10
VS 60V
R2
20
+
-
29
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-5
…. Cont”d
R1
10
VS 60V
R2
20
+ -
Power dissipated in R2
V22 VS
2
R2 R2
P2 = = = 180W=
602V2
20
= 360W
Power dissipated in R1
V12
R1
P1 = =VS
2
R1
602V2
10=
30
Chapter 6 – Power, Energy and Efficiency
IT2001PA Engineering Essentials (1/2)
Example 6-5
continue … ...
R1
10
VS 60V
R2
20
+
-
RT = R1 x R2
R1 + R2
10 x 2010 + 20 = = 6.67
PT = P1 + P2 = 360W + 180W = 540W
Total power dissipatedVS
2
RT
PT = = 540W= 602V2
6.67OR
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