et115-1

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Dr. Abdul Qadeer Polytechnic Institute Ellahabad

CH#1 Page 1

(Electron Theory)

(Matter)

106

(ii) (i)

(Proton)

(Nuclecus)

(Neutron)

(Shell) (Electrons)

1/1840

(Electrically Neutral)

19

1.602 10 C

(Elactrically Neutral)

(Electric Current And Ohms Law)

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CH#1 Page 2

(Elecrton Shells) NMLK (Shells) (Orbits)

M L K

n

2 = = K

8= = L

18= = M

8 (1) 18 (2)

32 (3)

(Energy Levels) (Allowed Energy Level)

K

(Valence Electrons)

8

(Free Electrons)

2 2

2 1 2n

2 2

2 2 2n

2 22 3 2n

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CH#1 Page 3

(Energy Bands)

(Band) (Overlap)

(Solid)

(Filled Band) (i)

(Full filled)

(Conduction Band) (ii) (Escape)

(Valance Band) (iii)

(Energies)

(Completely)

(Partially)

(Forbidden) (Forbidden) (Forbidden)

(External)

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CH#1 Page 4

"C" (Coulomb) "Q"

" "

(Electric Current) " I " (Rate) (Flow)

"A"

(Point) 1

2

(Insulator,Conductor,Semiconductror)

(Insulator)

4

(Conductor)

4

(Semiconductor)

4

(Electric Charge) (Excess) (Deficiency)

(Negatively Charged)

(Positively Charged)

Q It

QI

t

VI

R

I

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CH#1 Page 5

(Elecrton Current)

(Conventional Current)

(E.M.F) E.M.F

(Resistance)

"R"

1

2

(Potential and Potential Difference)

Q1 Q Q1 Q

(Ability) Q1 Q

(Work Done)

"V"

(Work) 1

2

VR

I

Volt=Joule/coulomb

V=IR

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CH#1 Page 6

(Ohm's Law)

(Resistivity) (Rho)

(Resistivity)

(Ohm-m) (Ohm-cm)

(Law's of Resistance)

" "

i

(Cross-Sectional Area)

ii

iii

(Temperature) iv

R

1R

A

1, R R R R

A A A

" "

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CH#1 Page 7

(Alloys) ii

iii

(Negative)

iv

(Effects of Temperature on Resistance)

i

(Ranges)

1

1

2

2

1 21 2

1 1

2 2

2 12

1

:

500

125

90

?

:

90 500360

125

Data

l m

R

R

l

Solution

l l R and R

a a

R l

R l

R ll m

R

Example: The resistance of 500 meter of a certain wire is 125 ohm. What length of the

same wire will have a resistance of 90 ohm.

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CH#1 Page 8

(Temperature Co-efficient)

0 C

R

t C

tR

0Changein Resistance, -t R R R

(i)

(ii) (iii)

0 0t R R R t

OR

0 0t R R t

0 (1 )t R t

0

0

: 40

50

0.0043 / 0

: (1 )

40(1 0.0043 50)

40 1.215 48.6

t

Data R

t

C at C

Solution R R t

1

1

2

2

2 2

1 1

2

2

2

: 10

15

?

30

0.0072 / 0

1:

1

1 0.0072 30

10 1 0.0072 15

1.21610

1.108

10.97

Data R

t C

R

t C

C at C

R tSolution

R t

R

R

R

Calculations about Temprature Co-efficient of Resistance

Example 1:The field winding of a generator has a resistance of 40 at 0& .What its

Resistance at 50C? Resistance-Temperature coefficient of copper is 0.0043/C at 0C.

Example 2: A column of mercury has a resistance of 10 at 15C. What will its resistance at

30C?The Resistance-Temperature coefficient of mercury is 0.0072/C at 0C.

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CH#1 Page 9

1

1

2

2

2 1 2 1

2

2

2

: 10

20

?

60

0.0039 / 20

: 1 (

10 1 0.0039(60 20)

10(1 0.0039 40)

11.56

Data R

t C

R

t C

C at C

Solution R R t t

R

R

R

1

1

2

2

2 2

1 1

2

2

2

2

2

2

: 55

20

65

?

0.004 / 0

1:

1

1 0.00465

55 1 0.004 20

1 0.0041.181

1.081.1818 1.08 1 0.004

1.2756 1 0.004

0.2756

0.004

69

Data R

t C

R

t

C at C

R tSolution

R t

t

t

t

t

t

t C

Example 3: A coil has a resistance of 10 at 20C. What is its resistance at 60C?

Resistance-Temperature coefficient at 20C= 0.0039/C .

Example 4:The shunt winding of DC generator has a resistance of 55 at 20C.After a run at

full load the resistance rise to 65. Find the average temperature of winding , Resistance-

Temperature coefficient of copper is 0.004/C at 0C.

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CH#1 Page 10

(Series Circuit of Resistance)

1

1

2

2

2 1

1 2 2 1

: 4010

48.25

60

?

:

48.25 40

40 60 48.25 10

8.25 8.252400 482.5 1917.5

0.0043/ 0

Data R

t C

R

t C

R RSolution

R t R t

C at C

Example 5:The Resistance of a coil wire increases from 40 at 10C to 48.25 at 60C.Find

temperature coefficient at 0C of conductor material.

Exercise 1

Q1: The resistanc of the shunt winding of a certain dynamo was 38 at a tempratur of 16C.

After a run of several hours the temprature increased to 45C. Determine the resistance of the

winding at this temprature. = 0.004 (42.143)

Q2: During a cirtain test upon a shunt wound motor ,it was found that the resistance of thefield coil 57.7. if the resistance before comencing the test was 52.5 at the temprature of

15C. Determine final temprature of the coils? (41.25C)

Q3: A shunt winding of a motor has a resistance of 80 at 15C. find its resistance at 50C?

Resistance-Temperature coefficient of copper 0.004/C at 0C. (90.57)

Q4: The R of a coil of wire increases from 40 at 10C to 48.25 at 60C. Find the

temprature co-efficent of the condultor material. (0.004125)

Q5: At 15C the resistance of the coil of copper of a dynamo is 250. After working 6 hours

on full load, the rasistance of the coil increase to 305

. What is rise temprature of the coil ?if the temprature cofficient is 0.004/C at 0C. (73.3C)

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CH#1 Page 11

(Characteristics) i

ii

iii

iv

v

vi

(Off)

vii

(Parallel Circuit of Resistance)

1 2 3 I I I I

1 2 3T R R R R

1 1 2 2 3 3, ,V IR V IR V IR

1 2 3tV V V V

1 2 3TP P P P

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CH#1 Page 12

(Characteristics)

i

ii

iii

iv

v

vi vii

1 2 3

1 2 3

, ,V V V

I I I R R R

1 2 3T I I I I

1 2 3

1 1 1 1

T R R R R

1 2 3TP P P P

1 2 3V V V V

(Voltage Divider Rule)

(Division of voltage in series circuit)

T 1

1 1 1 T

T 1 2

T 22 2 2 T

T 1 2

V RV =IR R V

R R +R

V RV =IR R V

R R +R

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CH#1 Page 13

(Division of voltage in parallel circuit)

(Current Divider Rule)

(Resistors)

(Resistance)

(Fixed Resistors) (i)

(corbon Composition Resistors) (a)(Wire-wound Resistors) (b)

(Thin Film Resistors) (c)(Thick Film Resistors) (d)

(Variable Resistors) (ii)

(Screw) (Knob) (Dial)

1 2

1 2 21

1 1 1 1 2

1 2

1 2 12

2 2 2 1 2

t

t t t

T

t

t t t

T

R RI

R RV I R RI I

R R R R R

R RI

R RV I R RI I

R R R R R

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CH#1 Page 14

(Potentiometers)

(a)

(Rheostates) (b)(Trimmers) (c)

(Colour Coding Of Resistors) (Bands)

(Left) (Tolerance)

(Numerical value) 54 (Right)

1

2

3 (Tolerance) 4

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CH#1 Page 15

Gold Green violet Red

510

1

2

3

1 2 3

1 2 3

1 1

2 2

3 3

: 2

3

6

4

?

?

, , ?

:

2 3 6 11

40.363

11

0.363 2 0.727

0.363 3 1.089

0.363 6 2.178

T

T

T

Data R

R

R

V V

R

I

V V V

Solution

R R R R

R

VI A

R

V IR V

V IR V

V IR V

27 5% = 27000005%

=2.7M5%

Calculation about series-parallel circuits

Example: Three resistances of 2, 3 and 6 are connected in series across 4 volt

supply. Find:

(a)Total Resistance (b) Current (c) Voltage drop across each resistor.

Exercise 2

Q1:A series circuit consisting of three resistors, 2,8 and 20,connected to a battery has a

current of 2A. What voltage exists across each resistor and also calculate the total voltage of

the battery . (4V.16V,40V,60V)

Q2: what value of resistor , connected in series with a 1.8K resistor, will result in a total

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CH#1 Page 16

resistance of 2K. (0.2K or 200)

Q3: Three resistors are connected in series. The value of the two resistors are 10K and

20K. The supply voltage are 200Volts. If the current following through the third resistor is

5mA, Find the value of the resistor. (10K)

Q4: Three resistors of 5K, 10K and 15K are connected in series across 24Voltagesource. Using voltage division Rule, Determine voltage drop across each resistance.

(4V, 8V, 12V)

Q5:Three resistors of 4ohms,6ohms and 8ohms respectively are connected in parallel. Find

equivalent resistance. (1.846)

Q6: Four resistance, each equal to 3.2ohms, are connected in parallel. Find the equivalent

resistance. (0.8ohms)

Q7: Two Resistance of 3.1ohms and 7.2ohms respectly are connected in parallel. Find the

equivalent resistance. (2.16ohms)

Q8:Find the total resistance of circuit shown. If the Total current taken by this circuit is 5A

what is the supply voltage. (3ohms,15volt)

Q9:A serch light taks 100A current at 80 Volts, it is to be oprated from 220V supply, Find the

value of the resistor to be connected in series. (1.4ohms)

Q10: Three Resistors are connected in parallel have an equivalent resistance 1.2 ohms, The

value of two of the resistors are 6 ohms and 12 ohms, Find the value of third. (1.71ohms)

Q11:A Resistor of 3.6ohm is connected in series with an other resistor of 4.56ohms, What

resistance must be placed across the one of 3.6 ohms so that the total reistance of the circuit

shell be 6 ohms. (2.4ohms)

Q12: A resistor of 3 ohms is connected in parallel with one of 2 ohms and in series with this

is a resistor of 4 ohms. What is the total resistance of circuit. (5.2ohms)

Q13:Find the totla resistance of circuit shown:

Q14:A factory is supplied by a substation through a pair of leads of total resistance of

0.08ohms. The total load is 250A at 200V. What voltage must be maintained at the

substation.

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CH#1 Page 17

Q15:Three resistors of 4 , 12 and 6 ohms are joined in parallel. If the total current taken is

12A, find the current through each. (6A,2A,4A)

Q16: Find the resistance of circuit shown:

Q17: For the network shown in the fig, The potential difference between A and C is 10V.

Calculate the current in each resistor.

(0.7A,2.1A,0.8A,2.0A)

Q18:Two Resistors of 4 ohm and 8 ohm are connected in parallel across a 6 volt battery.

Using Current division Rule determines the amount of current flowing through each resistor.

(1.5A, 0.75A)

Q19: In the circuit shown the current flowing in the 8 ohm resistor is 2.5 amperes.Find:

(a)Current in other resistors (b)The resistor X (c) The equivalent Resistance

(0.5A,0.8A,0.2A,100,5)

Q20: In the Circuit shown the current flow in X resistor is 1A. Find: (a) the current in each

resistors (b) The value of X (6A,8A,48)

Q21: In the series parallel circuit shown, find:

(a)Voltage across 4 ohm resistor (b) the supply voltage. (45V,140V)

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CH#1 Page 18

Q22: A resistance of 10 is connected in series with two resistance each of 15 arranged in

parallel.What resistance must be shunted across this parallel combination so that the total

current taken shall be 1.5A with 20V supply. (R=6)

Q23: Determine the value of R1,R2 and R3 in circuit shown. If R2=2R1 and R3=2R2 and total

resistance is 16K.

Q24: Given the information provided in circuit shown:

(a) Determine R3 (b) Calculate E. (s) Find Is (d) Find I2 (10,40V,10A,2A)

et115-1

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