Principle of EngineeringPrinciple of EngineeringResistance and its relation with potential difference Resistance and its relation with potential difference

and current, Ohm’s Lawand current, Ohm’s Law

Principle of EngineeringPrinciple of EngineeringResistance and its relation with potential difference Resistance and its relation with potential difference

and current, Ohm’s Lawand current, Ohm’s Law Electricity Session 2 (2 hours)Electricity Session 2 (2 hours)

Resistance

• Chinese dictionary: – 抵抗、阻擋、阻力

• English dictionary: – oppose; overcome

• Physics dictionary: – (measure of the) property of not

conducting heat or electricity ( 熱阻、電阻 )

Resistance

• A force (emf or voltage) is required to move electronics (e-) freely (current) in material.

• This force is to “oppose” or “overcome” “friction” that e- experience in moving between ionized atoms.

• The higher is the friction,– the larger is required force to maintain e- flow– the lower is e- flow rate per unit force

Resistance

• We call this friction the RESISTANCE• The measurement unit is OHM, or Ω.• A material has 1Ω when a voltage of

1V across it causes a current of 1A through it.

• All materials (gas, liquid, solid) have resistance, some are higher than others.

Georg Simon Ohm

Born: 16 March 1789 in Erlangen, Bavaria (now Germany)

Died: 6 July 1854 in Munich, Bavaria

More:http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/

Ohm.html           

Resistance (class work)

• Give an educated guess (i.e., with reason) on the resistance (High, Medium or Low) of materials in the RH table:

Material Ω

air

vacuum

mineral water

de-ionized water

rubber

platinum

Resistance

• All materials have RESISTANCE (R) • Some have very HIGH value

– They are insulators– They are to stop current flow and/or to isolate voltage

• Some have MEDIUM value– They are resistors – They are for signal processing and/or circuit design

• Some have very LOW value– They are conductors– They are for electric signal and/or energy transfer

Resistance

• Resistance of materials has the relationship:

R = ρℓ/A

• Does it make sense that R ∞ ℓ ?• Does it make sense that R ∞ 1/A ?• What is the physical meaning of ρ ?

Ohm’s Law (1)

• Let us determine the relationship between resistance (Ω), voltage (V) and current (A)– Construct a simple circuit with a variable

voltage source (V) and a fixed resistive load (R). Determine how the current (I) change with V value.

– Plot a suitable graph to show the relationship between V, I and R

– Put down your immediate observationHow to choose source and load

value?

Ohm’s Law (2)

• Redraw the graph (if necessary) with Voltage (V) as vertical axis and Current (I) as horizontal axis.– What is the relationship between V and I?– What is the significance of the graph

slope?– How does your experiment fit in with

Ohm’s Law: V = Ohm’s Law: V = I*RI*R y = m x

Resistor

• Resistors are produced with fixed or adjustable value. They are one of the most basic type of component in electronic circuits.

• Resistors have many functions: e.g. current limiting; voltage division; signal processing; … in a circuit.

• Resistor in a circuit MUST obey Ohm’s Law

Colour Representation of Resistance

1 2 3 4 5 6 8 9 07

1st color band – first digit value

2nd color band – second digit value

3rd color band – third digit value (for 1% R only)

4th color band – multiplier: color represent number of zeros after 2nd digit. Gold for 10-1, silver for 10-2

5th color band – tolerance: brown for 1%, red for 2%, gold for 5%, silver for 10%

6th color band – quality: color indicate failure rate/1000hr

Resistance

• Amount of current flows in an electric circuit depends on the resistance of the material through which it travels

I=V/R• A resistor is a device which provides resistance

in an electrical circuit

R=V/I

• SI unit is ohm, written as 1 =1 VA-1

• An electric circuit is a connection of sources and loads in any way which allow charge to flow.e.g. a simple circuit with a battery and

a light bulb

• Relationship between current direction and voltage polarity

V=____

V=_____

I

+ 10V -

• Consider the following circuit:

– What is the voltage VR through the 5 resistor, and its polarities?

– What is the current I, and its direction?

+

V

-

10+V-

5

VR

5

Measuring resistance

• Voltmeter-ammeter method

R=V/I

• Multimeter• What is the resistance of your body?

A

V

• An open circuit occurs when a conductor is broken between the points under test.

• A short circuit occurs when a low resistance conductor such as a wire is connected

R=____

R=____

Ohm’s Law

• Voltage across two ends of a resistor is directly proportional to the current flowing through it.

I

V

V-I graph for a resistor that obeys Ohm’s law

V=IRI

+ V -

Resistors in series

• A series circuit has only one path for current to flow– Example:

– Same current through each resistor I = I1 = I2

R2R1

+ V1- + V2 -

I

+ V -

I1 I2

– Applying Ohm’s law to each resistor,V1 = IR1, V2 = IR2

– Voltage of the source equals sum of V1 and V2

V = V1 + V2

= IR1 + IR2

= I (R1 + R2) = I R

– Equivalent resistance R = R1 + R2

– In general

R = R1 + R2 + R3 + • • • + Rn

R1 R2 R3

• • •Rn

• Example:

– What is the equivalent resistance?– What are the currents I1, I2 through the

resistors?– What are their directions?– What is the voltage across each

resistor?

Indicate the relative voltage polarities (+,-)

12V

2 4

V1 V2

I

I1 I2

• Solution:

– Equivalent resistance = 2 + 4 = 6– Current I = V/R = 12V/6 =2A

12V

2 4

12V

6

+ 12V -

2 4

I

I1 I2

• Solution:– V = IR

Voltage across 2 resistor = 2A*2 = 4V

Voltage across 4 resistor = 2A*4 = 8V

+ 12V -

2 4

+ 4V - + 8V -

I

I1 I2

• Consider the following circuit:

– What are the voltages V1, V2, V3, and V4, and their corresponding polarities 極性 ?

– What is the current? and its direction?

+

V

-

10

V1

5

V3

V2

V4

5

5 5

• Consider the following circuit:

– What are the voltages V1, V2, V3, and V4, and their corresponding polarities?

– What is the current, and its direction?

+

V

-

10

V1

5

V3

V2

V4

5

5 5

Resistors in Parallel

• A parallel circuit has more than one path for current to flow– Example:

– Same voltage across each resistorV = V1 = V2

R2

R1

+ V2 -

+ V1 -

I2

I1

+ V -I

– Applying Ohm’s law to each resistor,V = I1R1, V = I2R2

– Sum of current in branches equal to current I I = I1 + I2 = V/R1+V/R2

= V (1/R1+1/R2) = V 1/R

– Equivalent resistance 1/R = 1/R1+1/R2

– In general

1/R = 1/R1+1/R2+1/R3+ • • •+1/Rn

R1

R2

R3

Rn

...

• Consider the following with R1 > R2

What can be said about the equivalent resistance R ?

(a) R > R1

(b) R2 < R < R1

(c) R < R2

R1

R2

R

• Example:

– What is the equivalent resistance?– What are the currents through the resistors and

their directions?– What is the total current?

12V

2

4

• Solution:

– Equivalent resistance:1/R = 1/R1+1/R2 = 1/2 + 1/4 = 3/4

R = 4/3– Same voltage across each resistor = 12V

I1 =current through 2 =V/R1 =12V/2=6A

I2 =current through 4=V/R2=12V/4=3A

– Total current I = I1 + I2 = 6A + 3A = 9A

12V

2

4

12V

4/3

I

I1

I2

• Example:

– What is the equivalent resistance?

– What is the supply voltage (Vs)?

– What are the voltages across AB (VAB), BC (VBC)?

What are the currents through the resistors (I20, I30) ?

30unknown

voltage supply

10

20

B

C

A

2A+

V s

-

+ V AB -

+

V BC

-I20 I30

• Solution:

– Equivalent resistance

R = 22

30unknown

voltage supply

10

20

B

C

A

2A

unknown

voltage supply

10

12

B

C

A

2A

unknown

voltage supply

22

B

C

A

2A

• Solution:

– Supply voltage

Vs =IR=2A*22=44V– Voltage across AB,

VAB=2A*10 =20V

Voltage across BC, Vbc=V-VAB=44V-20V=24V

30unknown

voltage supply

10

20

B

C

A

2A

unknown

voltage supply

10

12

B

C

A

2A+

V s

-

+

V s

-

+ V AB - + V AB -

+

V BC

-

+

V BC

-

• Solution:

– Current through 20 resistor

I1 = VBC/ 20 = 1.2A

– Current through 30 resistor

I2 = VBC/ 30 = 0.8A

Check total current

I1 + I2 = 1.2A + 0.8A = 2A

30unknown

voltage supply

10

20

B

C

A

2A I1 I2

• Some problems to work in class:– Problem 1:

• What is the equivalent resistancebetween A and B?

3

9

9

B

A

9

3

3

– Problem 2:

• What is the equivalent resistance between A and B?

8

8

BA

8

8