Chap 6 bte1013

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Electricity And Electronics Fundamentals BTE 1113

Transcript of Chap 6 bte1013

Electricity And Electronics Fundamentals

BTE 1113

Chapter 6

Parallel Circuits

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Parallel Circuits

• House circuits contain parallel circuits• The parallel circuit will continue to operate even

though one component may be open• Only the open or defective component will no

longer continue to operate

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Parallel Circuits

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Parallel Circuits

• Elements in parallel– When they have exactly two nodes in common

• Elements between nodes – Any device like voltage sources, resistors, light

bulbs, etc.

• Elements connected in parallel– Same voltage across them

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Parallel Circuits

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Kirchhoff’s Current Law (KCL)

• The algebraic sum of the currents entering and leaving a node is equal to zero

0I

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Kirchhoff’s Current Law (KCL)

• Currents entering the node are taken to be positive, leaving are taken to be negative

• Sum of currents entering a node is equal to the sum of currents leaving the node

outin II

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Kirchhoff’s Current Law (KCL)

• An analogy: – When water flows in a pipe, the amount of

water entering a point is the amount leaving that point

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Direction of Current

• If unsure of the direction of current through an element, assume a direction

• Base further calculations on this assumption

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Direction of Current

• If this assumption is incorrect, calculations will show that the current has a negative sign

• Negative sign simply indicates that the current flows in the opposite direction

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Resistors in Parallel• Voltage across all parallel elements in a

circuit will be the same

• Total resistance of resistors in parallel will always be less than resistance of smallest resistor

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Parallel Resistors For resistors in parallel, the total

resistance is determined from

Note that the equation is for the reciprocal of RT rather than for RT. Once the right side of the equation has been

determined, it is necessary to divide the result into 1 to determine the total resistance

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Parallel Resistors

The total resistance of any number of parallel resistors can be determined using

The total resistance of parallel resistors is always less than the value of the smallest resistor.

N

T

RRRR

R1

...1111

321

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Equal Resistors in Parallel

• For n equal resistors in parallel, each resistor has the same conductance G

• GT = nG

• RT = 1/GT = 1/nG = R/n

• Total resistance of equal resistors in parallel is equal to the resistor value divided by the number of resistors

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Special Case: Two Resistors in Parallel

• For only two resistors connected in parallel, the equivalent resistance may be found by the product of the two values divided by the sum

• Often referred to as “product over the sum” formula

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21

RR

RRR

T

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Resistors in Parallel

• For a circuit with 3 resistors: IT = I1 + I2 + I3

GGGG

RRRR

R

E

R

E

R

E

R

E

T 321

321T

321T

1111

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Three Resistors in Parallel• For three resistors in parallel:

• Rather than memorize this long expression– Use basic equation for resistors in parallel

323121

321

RRRRRR

RRRR

T

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Voltage Sources in Parallel

• Voltage sources with different potentials should never be connected in parallel

• When two equal voltage sources are connected in parallel– Each source supplies half the required current

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Voltage Sources in Parallel

• Jump starting automobiles

• If two unequal sources are connected– Large currents can occur and cause damage

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Current Divider Rule

• Allows us to determine how the current flowing into a node is split between the various parallel resistors

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Current Divider Rule

yy

yy

IR

RI

IG

GI

RIRI

xx

yy

xx

xx

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Current Divider Rule

• For only two resistors in parallel:

T

TT

T

IRR

RI

R

RII

RR

RRR

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21

11

21

21

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Current Divider Rule

Tx

Tx I

R

RI

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Current Divider Rule

• If current enters a parallel network with a number of equal resistors, current will split equally between resistors

• In a parallel network, the smallest value resistor will have the largest current– Largest resistor will have the least current

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Current Divider Rule• Most of the current will follow the path of

least resistance

• For parallel elements of different values, the current will split with a ratio equal to the inverse of their resistor values

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Analysis of Parallel Circuits

• Voltage across all branches is the same as the source voltage

• Determine current through each branch using Ohm’s Law

• Find the total current using Kirchhoff’s Current Law

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Analysis of Parallel Circuits

• To calculate the power dissipated by each resistor, use either VI, I2R, or V2/R

• Total power consumed is the sum of the individual powers

• Compare with IT2RT

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Applications

Car system The electrical system on a car is essentially a

parallel system.

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Applications

House wiring Except in some very special circumstances

the basic wiring of a house is done in a parallel configuration.

Each parallel branch, however, can have a combination of parallel and series elements.

Each branch receives a full 120 V or 208 V, with the current determined by the applied load.

References

• Electricity and Electronics by Gerrish, Dugger and Roberts, 10th edition, 2009, GW Publisher

• Circuit Analysis: Theory and Practice by A. H. Robbins, W. C. Miller, 4th edition, 2006, Thomson Delmar Learning

• Introductory Circuit Analysis by R. L. Boylestad, 11th edition, 2007, Prentice Hall

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