Ee1 chapter6 power_energy&efficiency

Apr 15, 2023

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IT2001PAEngineering Essentials (1/2)

Chapter 6 – Power, Energy and Efficiency

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IT2001PA Engineering Essentials (1/2)

Lesson Objectives

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

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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

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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.

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Units

Unit of Voltage : Volts (v)

Unit of Current : Ampere (A)

Unit of Resistance : Ohms ()

Recall units

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Units

Unit of Charge: Coulomb (Q)

Unit of Energy : Joules (J)

Unit of Power : Watts or J/s (W)

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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

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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)

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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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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

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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

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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

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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

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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

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High power consumption

Low power consumption

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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

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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

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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

= + + … +

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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%

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Problem Solving

Power

Calculations

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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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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

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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

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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

+ -

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R1 = 10

VS = 60V

R2 = 20

+ -

RT = R1 + R2 = 10 + 20 = 30

IT =VS

RT

= 2A= 60V 30

Example 6-4…….cont”d

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Example 6-4 ….cont”d R1 = 10

VS = 60V

R2 = 20

+ -

Power dissipated in R1


P1 = IT2 x R1 = 22A2 x 10 = 40W

P2 = IT2 x R2 = 22A2 x 20 = 80W

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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

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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

+

-

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Example 6-5

…. Cont”d

R1

10

VS 60V

R2

20

+ -


V22 VS

2

R2 R2

P2 = = = 180W=

602V2

20

= 360W


V12

R1

P1 = =VS

2

R1

602V2

10=

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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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