Ee1 chapter6 power_energy&efficiency

IT2001PA
Engineering Essentials (1/2)

Chapter 6 – Power, Energy and Efficiency

Lecturer Name
lecturer_email@ite.edu.sg
Aug 16, 2012
Contact Number


Lesson Objectives
Upon completion of this topic, you should be able to:
 Calculate power and energy in electrical circuits..

IT2001PA Engineering Essentials (1/2) 2


Specific Objectives
1. State the units for :
 Quantity of electricity
 Energy
 Power
2. Establish the following equations :
 Q=Ixt
 E=Pxt
3. Establish the following equations of power
 P = I2 x R = V2/R = V x I



Specific Objectives
4. Solve simple problems involving a maximum of three
resistors relating to :
 Quantity of electricity
 Electrical energy
 Electrical power
4. Calculate energy consumption of an electrical load in
kWh.
5. Calculate the cost of energy consumed by an electrical
load for a given power and time.
6. Convert the unit from kWh to Joules and vice versa.



Units

Recall
units
 Unit of Voltage : Volts (v)

 Unit of Current : Ampere
(A)

 Unit of Resistance : Ohms
(Ω)



Units

 Unit of Charge: Coulomb (Q)

 Unit of Energy : Joules (J)

 Unit of Power : Watts or J/s (W)



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 Watt-seconds=Joules
= 3,600,000 Joules
= 3.6 MJ



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)



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



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
+ -



What is Energy
 Heat energy produced in the resistor is proportional
to :

a) square of the current - I 2
b) resistance of the resistor - R
c) duration of time - t in seconds

Energy = I2Rt joules
= Power x Time



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



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



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



Low power
consumption

High power
consumption



Equations of Power
 As power is work done per sec therefore
P = IR2t
t

P = I2R
P= V 2
R = V2
Ohm’s law
R R
I = V/ R
R = V/ I
= I
2 V = VI
I



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



Comparison

SERIES PARALLEL
IT = I1 = I2 = I3 = … = In IT = I 1 + I 2 + I 3 + … + I n
VS = V1 + V2 + V3 + … + Vn VS = V1 = V2 = V3 = … = Vn

RT = R1 + R2 + R3 + … + Rn 1 1 1 1 1
= + + …+
RT R1 R2 R3 Rn
PT = P1 + P2 + P3 + … … + Pn



Efficiency
 The efficiency of an electric circuit is the ratio of output to
the input expressed in percentage. It is symbolized by η.
 Efficiency of electric circuit,

 Output power is always smaller than input due to losses 
 Efficiency is always < 100%



Problem Solving

Power
Calculations



Example 6-2 (Efficiency)
The output of a generator is 1500W and the input is
equivalent to 1900W.
Calculate its percentage efficiency.

η= (1500/1900)x100 = 78.9%



Example 6-3

 Calculate the total power consumed by the circuit
below (i.e. the power dissipated in R).

Vs +
R
R=20Ω
60V
-

Power dissipated in R
V2 602V2
P = = = 180W
R 20Ω



Example 6-3
… cont”d

Vs R
60V 20Ω

V 60V
I = = = 3A
R 20Ω

Power dissipated in R
P = I2 x R = 32A x 20Ω = 180W



Example 6-4

 Calculate the power dissipated in R1 , R2 and
the total power consumed by the circuit below.

R1 = 10Ω R2 = 20Ω

+ -
VS = 60V



Example 6-4
…….cont”d
R1 = 10Ω R2 = 20Ω

+ -
VS = 60V
RT = R1 + R2 = 10Ω + 20Ω = 30 Ω
IT = VS = 60V = 2A
RT 30Ω



Example 6-
4
….cont”d R1 = 10Ω R2 = 20Ω

+ -

VS = 60V
Power dissipated in R1
P1 = IT2 x R1 = 22A2 x 10Ω = 40W
P2 = IT2 x R2 = 22A2 x 20Ω = 80W



Example 6-4
….. Cont”d
R1 = 10Ω R2 = 20Ω

+ -
VS = 60V

Total power dissipated
PT = IT x VS = 2A x 60V = 120W
or PT = P1 + P2 = 40W + 80W = 120W



Example 6-5

 Calculate the power dissipated in R1 , R2 and the
total power consumed by the circuit below.

+
VS R1 R2
60V - 10Ω 20Ω



Example 6-5
…. Cont”d

VS + R1 R2
60V - 10Ω 20Ω

V1 2 VS2 602V2 = 360W
P1 = = = 10Ω
R1 R1
V22 VS 2 602V2
P2 = = = = 180W
R2 R2 20Ω



Example 6-5
 c
o + R1 R2
n VS
10Ω 20Ω
t 60V -
i
n R1 x R 2 10Ω x 20Ω
u RT = = = 6.67 Ω
R1 + R 2 10Ω + 20Ω
e
Total power dissipated
VS 2 602V2
… PT = =
RT 6.67Ω = 540W
.O PT = P1 + P2 = 360W + 180W = 540W
.R
.



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Ee1 chapter6 power_energy&efficiency

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