chapter 5 - parallel circuits - i-shou university ee 2 c.y. lee objectives identify a parallel...
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2ISU EE C.Y. Lee
Objectives
Identify a parallel circuitDetermine the voltage across each parallel branchApply Kirchhoff’s current lawDetermine total parallel resistanceApply Ohm’s law in a parallel circuitUse a parallel circuit as a current dividerDetermine power in a parallel circuit
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Voltage in Parallel Circuits
The voltage across any given branch of a parallel circuit is equal to the voltage across each of the other branches in parallel
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Voltage in Parallel Circuits
Example: Determine the voltage across each resistor
V1 = V2 = V3 = V4 = V5 = 25 V
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Kirchhoff’s Current Law (KCL)
The sum of the currentsinto a node is equal to the sum of the currents out of that node
IIN(1) + IIN(2) + . . . + IIN(n)
= IOUT(1) + IOUT(2) +. . . + IOUT(m)
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Generalized Circuit Node Illustrating KCL
IIN(1) + IIN(2) + . . . + IIN(n) = IOUT(1) + IOUT(2) + . . . + IOUT(m)
or IIN(1) + IIN(2) + . . . + IIN(n) − IOUT(1) − IOUT(2) − . . . − IOUT(m) = 0
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Kirchhoff’s Current Law
Example: Determine the current through R2
I2 = 100 − 30 − 20 = 50 mA
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Total Parallel ResistanceThe total resistance of a parallel circuit is always less than the value of the smallest resistor
1/RT = 1/R1 + 1/R2 + 1/R3 + . . . + 1/Rn
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Total Parallel Resistance
Example: Calculate the total parallel resistance
321
1111RRRRT
++=
321
1111
RRR
RT
++=
321 RRRRT =
RT = 1/((1/100) + (1/47) + (1/22)) = 13.0 Ω
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Application of a Parallel Circuit
One advantage of a parallel circuit over a series circuit is that when one branch opens, the other branches are not affected
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Application of a Parallel Circuit
All lights and appliances in a home are wired in parallelThe switches are located in series with the lights
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Ohm’s Law in Parallel Circuits
V = IR, I = V/R, and R = V/I
Example: Find the each current in below circuit
RT = 1/(1/100 + 1/56)= 35.9 Ω
IT = VS/RT= 10/35.9 = 279 mA
IR1 = 10/100 = 100 mAIR2 = 10/56 = 179 mA
IR1 IR2
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Current Dividers
A parallel circuit acts as a current divider because the current entering the junction of parallel branches “divides” up into several individual branch currents
ITI1
I2
IT
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Current-Divider Formulas for Two Branches
ITI1
I2
IT
• The total current divides among parallel resistors into currents with values inversely proportional to the resistance values
21
2111 RR
RRIRIRI TTT +==
21
21
RRRRRT +
=⇒= 21 RRRT
( )TIRR
RI21
21 +=
( )TIRR
RI21
12 +=
16ISU EE C.Y. Lee
Current-Divider Formulas for Two Branches
Example: Find the each current in below circuit
I1 = 10(1000/(100+1000)) = 9.09 mA
I2 = 10(100/(100+1000)) = 0.909 mA
I1
I2
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General Current-Divider Formula
General current-divider formula for any number of parallel branches
( )TX
TX I
RRI =
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Power in Parallel CircuitsTotal power in a parallel circuit is found by adding up the powers of all the individual resistors, the same as for series circuitsPT = P1 + P2 + . . . + Pn
ST IVP =
TT RIP 2=
T
ST R
VP2
= RT = 1/(1/68 + 1/33 + 1/22) = 11.1 Ω
PT = (2)2(11.1) = 44.4 W
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Open Branches
When an open circuit occurs in a parallel branch, the total resistance increases, the total currentdecreases, and the same current continues through each of the remaining parallel paths
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Open Branches
When a lamp filament opens, total current decreases, the other branch currents remain unchanged
4I 3I
I I II I II
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Summary
A parallel circuit provides more than one path for currentThe total parallel resistance is less than the lowest-value parallel resistorThe voltages across all branches of a parallel circuit are the sameKirchhoff’s Current Law: The sum of the currents into a node equals the sum of the currents out of the nodeKirchhoff’s Current Law may also be stated as: The algebraic sum of all the currents entering and leaving a node is zero
22ISU EE C.Y. Lee
Summary
A parallel circuit is a current dividerThe total power in a parallel-resistive circuit is the sum of all the individual powers of the resistors making up the parallel circuitIf one of the branches of a parallel circuit opens, the total resistance increases, and therefore the total current decreasesIf a branch of a parallel circuit opens, there is no change in current through the remaining branches