1.1.5 CircuitTheoryLaws-1.pptx

Circuit Theory Laws

© 2014 Project Lead The Way, Inc. Digital Electronics

Circuit Theory Laws

This presentation will

• Review voltage, current, and resistance.

• Review and apply Ohm’s Law.

• Review series circuits.

o Current in a series circuit

o Resistance in a series circuit

o Voltage in a series circuit

• Review and apply Kirchhoff’s Voltage Law.

• Review parallel circuits.

o Current in a parallel circuit

o Resistance in a parallel circuit

o Voltage in a parallel circuit

Electricity – The Basics

An understanding of the basics of electricity

requires the understanding of three fundamental

concepts.

•

_Voltage

•

_Current

•

Resistance

A direct mathematical relationship exists between

voltage, resistance, and current in all electronic

Voltage, Current, & Resistance

4

Andre Ampere

1775-1836

French Physicist

Current – Current is the flow of electrical

charge through an electronic circuit. The

direction of a current is opposite to the

direction of electron flow. Current is

Voltage

5

Alessandro Volta

1745-1827

Italian Physicist

Voltage – Voltage is the electrical force that

causes current to flow in a circuit. It is

Resistance

Georg Simon Ohm

1789-1854

German Physicist

Resistance – Resistance is a measure of

opposition to current flow. It is measured in

First, An Analogy

7

Force

The flow of water from one tank to another is a good analogy for

an electrical circuit and the mathematical relationship between

voltage, resistance, and current.

Force: The difference in the water levels ≡ Voltage

Flow: The flow of the water between the tanks ≡ Current

Opposition: The valve that limits the amount of water ≡ Resistance

Flow

- +

Anatomy of a Flashlight

D - Cell

D - Cell

Switch _Switch

Light

Bulb Light_Bulb

Battery

Battery

Flashlight Schematic

• _{Closed circuit (switch closed)} • _{Current flow}

• _{Lamp is on}

• _{Lamp is resistance, uses}

energy to produce light (and heat)

• _{Open circuit (switch open)} • _{No current flow}

• _{Lamp is off}

• _{Lamp is resistance, but is not}

using any energy

9

- + - +

Current

Voltage

Current Flow

•

_{Conventional Current}

_assumes

that current flows out of the

positive side of the battery,

through the circuit, and back to

the negative side of the battery.

This was the convention

established when electricity was

first discovered, but it is incorrect!

•

_{Electron Flow}

_{is what actually}

happens. The electrons flow out

of the negative side of the battery,

through the circuit, and back to

the positive side of the battery.

Electron Flow

Conventional Current

Engineering vs. Science

•

_{The direction that the current flows does not affect what the}

current is doing; thus, it doesn’t make any difference which

convention is used as long as you are consistent.

•

_Both

_{Conventional Current}

_and

_{Electron Flow}

_{are used. In}

general, the science disciplines use

Electron Flow,

whereas

the engineering disciplines use

Conventional Current.

•

_{Since this is an engineering course, we will use}

Conventional Current

.

11

Electron Flow

Conventional Current

Ohm’s Law

•

_{Defines the relationship between voltage, current, and}

resistance in an electric circuit

•

_{Ohm’s Law:}

Current in a resistor varies in direct proportion to the voltage applied to it and is inversely proportional to the resistor’s value.

•

_{Stated mathematically:}

Where: I is the current (amperes)

V is the potential difference (volts) R is the resistance (ohms)

V

I R

+

-R

V

I



Ohm’s Law Triangle

V I R

V I R

V I R

)

A

,

amperes

(

R

V

I



)

,

ohms

(

I

V

R





)

V

,

volts

(

R

I

V



Example: Ohm’s Law

Example:

The flashlight shown uses a 6 volt battery and has a bulb with a resistance of 150 . When the flashlight is on, how much current will be drawn from the battery?

Example: Ohm’s Law

Example:

The flashlight shown uses a 6 volt battery and has a bulb with a resistance of 150 . When the flashlight is on, how much current will be drawn from the battery?

Solution:

15

V_T = +

-V_R

I_R Schematic Diagram

V I R

mA

40

A

0.04

150

V

6

R

V

I

R









Circuit Configuration

Series Circuits

• _{Components are connected}

end-to-end.

• _{There is only a single path for}

current to flow.

Parallel Circuits

• _{Both ends of the components are}

connected together.

• _{There are multiple paths for}

current to flow.

16

Components

Components in a circuit can be connected in one

of two ways.

Series Circuits

Characteristics of a series circuit

• _{The current flowing through every series component is equal.}

• The total resistance (R_T) is equal to the sum of all of the resistances

(i.e., R₁ + R₂ + R₃).

• The sum of all of the voltage drops (V_R1 + V_R2 + V_R2) is equal to the

total applied voltage (V_T). This is called Kirchhoff’s Voltage Law.

17 V_T

+

-V_R2 +

-V_R1

+

-V_R3 +

-R_T I_T

Example: Series Circuit

Example:

For the series circuit shown, use the laws of circuit theory to calculate the following:

• The total resistance (R_T)

• The current flowing through each component (I_T, I_R1, I_R2, and I_R3) • The voltage across each component (V_T, V_R1, V_R2, and V_R3)

• Use the results to verify Kirchhoff’s Voltage Law.

18 V_T

+

-V_R2 +

-V_R1

+

-V +

-R_T I_T

I_R1

I_R3

Example: Series Circuit

Current Through Each Component:

             k 1.89 1890 R k 1.2 470 220 R R3 R2 R1 R T T T mAmp 6.349 I I I I : circuit series a is this Since mAmp 6.349 k 1.89 v 12 I Law) s (Ohm' R V I R3 R2 R1 T T T T T        

Example: Series Circuit

Solution:

Voltage Across Each Component:

V I R volts 7.619 Ω K 1.2 mA 6.349 V Law) s (Ohm' R3 I V volts 2.984 Ω 470 mA 6.349 V Law) s (Ohm' R2 I V volts 1.397 Ω 220 mA 6.349 V Law) s (Ohm' R1 I V R3 R3 R3 R2 R2 R2 R1 R1 R1                

Example: Series Circuit

Solution:

21

Verify Kirchhoff’s Voltage Law:

v 12 v

12

v 619 . 7 v 984 . 2 v 397 . 1 v 12

V V

V

V_{T R1 R2 R3}



 



 

Parallel Circuits

Characteristics of a Parallel Circuit

• _{The voltage across every parallel component is equal.}

• The total resistance (R_T) is equal to the reciprocal of the sum of the

reciprocal:

• The sum of all of the currents in each branch (I_R1 + I_R2 + I_R3) is equal

to the total current (I_T). This is called Kirchhoff’s Current Law.

22 + -+ -V_R1 +

-V_R2 V_R3

R V_T I_T + -3 2 1 T 3 2 1 T R 1 R 1 R 1 1 R R 1 R 1 R 1 R 1      

Example: Parallel Circuit

Example:

For the parallel circuit shown, use the laws of circuit theory to calculate the following:

• The total resistance (R_T)

• The voltage across each component (V_T, V_R1, V_R2, and V_R3)

• The current flowing through each component (I_T, I_R1, I_R2, and I_R3) • Use the results to verify Kirchhoff’s Current Law.

23 23

+

-+

-V_R1

+

-V_R2 V_R3

R_T V_T

I_T

+

Example: Parallel Circuit

Solution:

Total Resistance:

Voltage Across Each Component:

volts 15 V V V V : circuit parallel a is this Since R3 R2 R1

T    

           59 . 346 R k 3.3 1 k 2.2 1 470 1 1 R R 1 R 1 R 1 1 R T T 3 2 1 T

Example: Parallel Circuit

Solution:

25

V I R

Current Through Each Component:

mAmp 43.278 346.59 v 15 R V I mAmp 545 . 4 k 3.3 v 15 R3 V I mAmps 6.818 k 2.2 v 15 R2 V I mAmps 31.915 470 v 15 R1 V I Law) s (Ohm' R1 V I T T T R3 R3 R2 R2 R1 R1 R1 R1                 

Example: Parallel Circuit

Solution:

Verify Kirchhoff’s Current Law:

mAmps 43.278

mAmps 43.278

mA 545 . 4 mA 818 . 6 mA 31.915 mAmps

43.278

I I

I

I_{T R1 R2 R3}



 

 

 

Summary of Kirchhoff’s Laws

27

Kirchhoff’s Voltage Law (KVL):

The sum of all of the voltage drops in a

series circuit equals the total applied

voltage.

Gustav Kirchhoff 1824-1887 German Physicist

Kirchhoff’s Current Law (KCL):

The total current in a parallel circuit equals

the sum of the individual branch currents.