a. basic concepts

7/30/2019 A. Basic Concepts

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COURSE OUTLINE

10. Fundamental of inductors and capacitors

1. Definitions of Basic Electrical quantities; systems of units; circuit

components.2. Ohms laws and Kirchhoffs laws

3. Analysis of series, parallel, series-parallel circuits

4. Resistance bridge circuits

5. Biasing circuits using resistive elements; design problems6. Voltage divider circuits; design problems

7. Analysis of resistive circuits with controlled sources

8. Circuit analysis techniques and network theorems

9. Practical sources


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15. Complete response of second order dynamic circuits with DC

excitation

11. Forced response of RL and RC circuits with DC excitation

12. Natural response of RL and RC circuits with non- zero initial conditions

13. Complete response of RL and RC circuits

14. Analysis of second order dynamic circuits

COURSE OUTLINE


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REFERENCES

5. Electric Circuits

Nilsson and RiedelPearson Prentice Hall, 7th Edition,

2005

1. Fundamentals of Electric Circuits

C.K. alexander & M.N.O. Sadiku

McGraw Hill, 2nd Edition, 2007

2. Introduction to Electric Circuits

Dorf and Svoboda,

John Wiley & Sons, Inc., 6th

Edition 2006

3. Principles of Electric Circuits

Thomas L. Floyd

Prentice Hall, 7th Edition 2006

4. Engineering Circuit analysisW. Hayt, Jr, et al

McGraw Hill, 7th Edition 2007


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t0 2 time

v(t)Vs

4

DC Voltage

AC Voltage

time

v(t)Vp


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Units and Prefixes

Variable Symbols Unit Unit

abbreviationTime t Second S

Charge Q Coulomb C

Current I Ampere A

Voltage V (or E) Volt V

Energy W Joule J

Power P Watt W

Resistance R Ohm

Conductance C siemens S


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Value Prefixes Abbreviation

10-12 Pico p

10-9 Nano n

10-6 Micro

10-3 Milli m

103 Kilo k

106 Mega M

109 Giga G

1012 tera T

Prefixes in SI units


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Charge

is a quantity of electricity. Negatively charge electrons constitutethe movement of charge within conductors, and the chargeassociated with one electron is Q = 1.6 x 10-19 C.

Current

is the rate of flow of electrical charge

a current flow of one ampere represents the movement of chargepast a given point equal to 1 coulomb per second (C/s)

Volt

I = ampere =

is a unit of potential difference, which is equal to one joule of workdone per one coulomb of charge.

volt = V =


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v(t)

-

+

Vs(t)v(t) expressed in

terms of othernetwork voltages

or currents

+

-

Vs(t)

v(t) a given

function oftime

Independent Voltage

Source

Voltage Source

Voltage/currentDependent

Voltage Sources:


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i(t) i(t)

Independent Current

SourceCurrent Source

Voltage/current

Dependent

i(t) expressed in

terms of other

network voltagesor currents

i(t) a given

function of

time

Current Sources:


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Resistance, R

is defined as the opposition to current flow exhibited by anydevice in which the resulting power is dissipated.

i(t)

Rv(t)

+

-

Resistance

)()( tRitv

Conductance, G It is the reciprocal of the resistance. Expressed in

mho/Siemens (S).


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Short Circuits

A short circuit is a direct connection between two points.

Open Circuits An open circuit represents the complete lack of a connection, it

can be described by the statement that the current flowingbetween the two points is zero.

Short

Circuits

open

Circuits


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Resistance of Wires

R L A V

-m m m2 m3

-cm cm cm2 cm3

-CM/ft ft CM

Circular mil (CM) area of a circle having a diameter of 1 mil. (1 mil = 0.001 inch)


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Effects of Temperature in Resistance

Note: Resistance of wires generally used in practice in electrical system increases

as temperature increases.

R2

R1

t2

t1Ttime, t

Resistance, R


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A Simple DC Circuits

+

-R

+

-R

closed circuits

open circuits

SW

E E

I


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An electric current requires a source ofelectromagnetic force oremf(a chargepump) - e.g. battery or power supply.

A battery or power supply hasan internal resistance, r,

making the measured terminal

voltage Vab when current is

flowing less than the emf, E.


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Ohms law

state that the current is directly proportional to the voltage acrossthe resistance and inversely proportional to the resistance.

I = R= E = RI

Current = Resistance = voltage = resitance x current

Where: R = resistance of resistor (ohm)

I = current drawn (ampere)

E = voltage across the resistor (volt)


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Power & Energy

Power Delivered when the current is leaving the positive terminal of

a device, that device is delivering power

Electrical

device

I

E

+

-

Power Absorbed

when the current is entering the positive terminalof a device, that device is absorbing power

ElectricaldeviceE

+

-

I

Energy

is the actual work performed or the capacityto perform work.

Power

is the rate of consuming energy


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Power Relationship

P = P = I2RP = VI

Where: P = power drawn (watts)

I = current drawn (ampere)

E = voltage across the resistor (volt)R = resistance of resistor (ohm)

W = energy (joules)

t = time 9seconds)

W = Pt


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Formula Chart:


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BASIC CIRCUIT LAWS

1) Kirchoffs Current Law [KCL]:

NODE

i1

i4

i3

i2

i1 - i2 - i3 + i4 = 0

0k

ki

i1

i2 = - i1

The algebraic sum of the currents at any node is zero. A node is ajunction point between two or more branches.


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2) Kirchhoffs Voltage Law [KVL]:

0k

kv

The algebraic sum of the voltages around any closed loop is zero.

a

v2

+

v1

-

++

++

--

- -c d

egcommon

b

vC

vLvR

iR

iC

iL021 vvvv LR

01 CR vvv

02 CL vvv

abcdega:

abcga:

edcge:


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SERIES CIRCUIT E1 = I R1E2 = I R2E3 = I R3

R1 b

+ -

baa R2RN R

+ ++ -- -

i1 i2 iN i

Equivalent Resistances

Resistors in series dividethe total voltage inproportion to theirmagnitudes.


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BASIC RULES:

Total Current, IT

Current- The current (A) is the same at any point in the circuit

IIIIN

21

Total Resistance, RT

Total resistance- The total resistance (R

T) is the sum of the

individual resistors

TNRRRR

21

Total Voltage, ET

The applied voltage (ET)is equal to the sum of the voltage drops

across all the resistors

TNEEEE

21


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TNPPPP

21

Total Power, PT

BASIC RULES:

The total power (PT)is equal to the sum of the power absorbed

across each resistors


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Voltage Divider Rule

R1

i

+

R2

+ +

-

+

-

-

-

ET

E2

Applying basic circuit laws :1

21

2

2E

RR

RE

E1

+

-


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PARALLEL CIRCUIT

RTE

IT

321

321

321

32

1111

111

RRRR

R

E

RRRE

R

E

R

E

R

E

IIII

eq

eq

i

Resistors in parallel divide thetotal current in inverseproportion to their magnitudes.


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BASIC RULES:

Total Current, IT

Current- The total current (A) is equal to the sum of the currentpassing through each resistor

Total Resistance, RT

Total resistance- The total resistance (RT) of the circuit is thereciprocal of the sum of the reciprocals of theindividual branches.

NIIII

21

nT RRRR

1111

21


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Total Voltage, ET

The voltagedrop across any branch of a parallel circuit is thesame as the applied voltage (ET)

NTEEEE ....

21

NTPPPP ....

21

Total Power, PT

The total power (PT)is equal to the sum of the power absorbed

across each resistors


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Current Divider Rule

Analysis using basic circuit

laws :

iRR

Ri

21

21

R1

i

+

R2

+

+

--

-

E i1 i2

iRR

Ri

21

12

Note : The larger current goes through the smaller resistor


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Series/Parallel Circuits

This circuit is composed of

two resistance segments: R1 alone

R2 and R3 in parallel

Resistors R2 and R3 can be

combined to form a singleequivalent resistance, R2,3:

This leave a simple seriescircuit


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This circuit is composed of

two resistance segments: R1 and R2 in series

R3 in parallel

Resistors R1 and R2 can becombined to form a singleequivalent resistance,R1,2:

This leaves a simpleparallel circuit.

Parallel/Series Circuits


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1. Find the current in a conductor through which 2.5 x 1020 free electrons pass is

8 sec.2. Determine the total charge entering a terminal between 1 sec and 2 sec if the

current passing the terminal is given by the equation i = 3t2 t, amperes.

3. A 500 ft. solid copper conductor has a diameter of 0.128 inch. What is its

resistance?

4. A piece of wire of uniform cross section has resistance of 0.8 . If the length of

the wire is doubled and its area of cross section is increased four times, what isits resistance? The temperature variation of resistance may be neglected.

5. A length of wire has a diameter of 11.7 mm and a resistance of 31 m. This

wire is passed through a series of drawing process reducing its diameter to 5

mm. Determine its resistance after.

6. A given wire has a resistance of 4 . Find the resistance of another wire,

having the same material as the first but having diameter twice as much?

EXAMPLE A


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EXAMPLE B

1. A 1.5 KW electric heater is connected to a 120-V source. (a) How much

current does the heater draws? (b) If the heater is on for 45 minutes, how

much energy is consumed in kilowatt-hours (kWh)? (c) Calculate the cost of

operating the heater for 45 minutes if energy costs 10 cents/kWh.

2. When connected to 110-V lines, a stove element takes 8 A. Calculate how

much power the element is consuming?

3. A 1.2 kW toaster takes roughly 4 minutes to heat four slices of bread. Find the

cost of operating the toaster once per day for 1 month (30 days). Assumeenergy costs 9 cents/kWh.

4. A flashlight battery has a rating of 0.8 ampere-hours (Ah) and a lifetime of 10

hours. (a) How much current can it deliver? (b)How much power can it give of

its terminal voltage is 6 V? (c) How much energy is stored in the battery in

kWh?

5. A 30-W incandescent lamp is connected to a 120-V source and is left burningcontinuously in an otherwise dark staircase. Determine: (a) the current through

the lamp, (b) the cost of operating the light for one non-leap year if electricity

costs 12 cents per kWh.


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1. A coil has a resistance of 20 ohms at 25C. Find its resistance at

65C. Resistance temperature coefficient at 25C is 0.00385 perC.2. The current in an electric lamp is 5 amperes. What quantity of

electricity flows towards the filament in 6 minutes?

3. One kilometer of copper wire, 1 square centimeter in cross section

has a resistance of 0.043 . Find the resistance of a wire 42.6 m long

and 0.005 cm2

in cross section.4. A length of wire has a resistance of 6 . What is the resistance of a

wire of the same material three times as long as twice the cross

sectional area?

5. The resistance of 500 meters of a certain wire is 125 . What length

of the same wire will have a resistance of 90 .

6. A current of 30 A divides between three resistances in parallel, 60 10

and 12 ohms respectively. What is the current in the 10 ohm

resistance?

ASSIGNMENT 1


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EXAMPLE C

1. Two resistors connected in series have an equivalent resistance of 690

ohms. When they are connected in parallel, their equivalent resistance is

150 ohms. Find the resistance of each resistor.

2. When two unknown resistors are connected in series with a battery, 225

W is dissipated with a total current of 5 A. For the same total current, 50

W is dissipated when the resistors are connected in parallel. Determine

the values of the resistors.

3. A 5 ohm resistor and a 10 ohm resistor are connected in series. If thepower dissipated in the 5-ohm resistor is 125 W, what is the potential

difference across the combination?


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EXAMPLE C

4. Find RT, IT, IR1, IR2, & IR3. 5. Find: a. RT & IT,

b. IR1, IR2 & IR3;

c. ER1, ER2 & ER3


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EXAMPLE C

6. Given:

Find: IR1, IR2, IR3 & IT

7. Three resistors A, B and C are

connected in parallel and take atotal current of 7.9 amps. Resistor

A takes 2.5 amp and has a

resistance of 48 ohms; also, the

current through B is twice as

much as that through C. Calculate

(a) IB and IC (b) the line voltage,(c) RB and RC.


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EXAMPLE D

1. A resistance of 10 is connected in series with two resistances each 15

arrange in parallel. What resistance must be shunted across this parallelcombination so that the total current taken shall be 1.5 A with 20 V applied?

2. Two lamps of 80 W and 60 W rated 200 V supply are connected to 400 v supply

mains in series. Find the value of additional resistance to be connected across

60 W to get 200 V on each lamp.

3. A 10-ohm and a 20-ohm resistance are connected in parallel. Another resistance

of 5-ohm is connected in series with the two. If the supply voltage is 48 volts,what is the current through the 10-ohm resistance?

4. A resistor of 40 ohms is in series with two resistors A and B in parallel. The

resistance of A is 100 ohms. The entire series-parallel circuit is connected

across a 120-V supply. Determine the resistance of resistor B in order that the

total current be 1.2 A.

5. A 12-ohm resistor is connected in parallel with a series combination of resistorsof 8 and 16 ohms. If the drop across the 8-ohm resistor is 48 V, determine the

total current.


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1. A lamp rated 100 V, 75 A is to be connected across 230 V by connecting a series

resistor to it. Determine the power dissipated in the series resistor.

2. Two heating coils in series draws 5 A from a battery. The first coil, when usedalone, is found to draw 8 A from the same battery. What current will be drawn by

the second coil when used alone?

3. Four 60W, 110 V bulbs are to be operated from a 230 v source. Determine the

value of the resistance connected in series with the line so that the voltage

across the bulbs does not exceed 110 V.

4. When the series combination of R1 and R2 is connected across a 30 V source,the current drawn is 10 A. If R2 is replaced by R3, the current is 12 A. The three

resistors in series draws 6 A. Determine the value of R3.

5. Four 60-W, 110-V bulbs are to be operated from a 230-V source. Determine the

value of the resistance connected in series with the line so that the voltage

across the bulbs does not exceed 110 V.

6. Two 30 ohm resistors are connected in series. When a resistor R is connected

across one of them, the total circuit resistance is 40 ohm. Calculate the ohmic

value of R.

ASSIGNMENT 2


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a. basic concepts

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