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7/30/2019 Lecture7 Series and Parallel
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Online Resource for ETCH 213
Faculty: B. Allen
Introduction to Series-Parallel DC Circuits
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Online Resource for ETCH 213
Faculty: B. Allen
Series-parallel circuit
A network or circuit that contains components
that are connected in both series and parallel.
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Online Resource for ETCH 213
Faculty: B. Allen
Series-parallel resistive circuits
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Online Resource for ETCH 213
Faculty: B. Allen
Tracking current through a
series-parallel circuit
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Online Resource for ETCH 213
Faculty: B. Allen
Total resistance in a series-
parallel circuitStep 1: Determine the equivalent resistance of all
branch series-connected resistors.
Step 2: Determine the equivalent resistance of allparallel-connected combinations.
Step 3: Determine the equivalent resistance of the
remaining series-connected resistors.
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Online Resource for ETCH 213
Faculty: B. Allen
Calculating total resistance
Find the equivalent resistance for R5 and R6.
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Online Resource for ETCH 213
Faculty: B. Allen
Find the equivalent resistance for R4
and R5-6
.
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Online Resource for ETCH 213
Faculty: B. Allen
Find the equivalent resistance for R2, R3, and R4-5-6.
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Online Resource for ETCH 213
Faculty: B. Allen
Find RT.
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Online Resource for ETCH 213
Faculty: B. Allen
Voltage division in a series-
parallel circuitFind:
V1
V2
V3
V4
V5
V6
V7
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Online Resource for ETCH 213
Faculty: B. Allen
R3-4 = R3 + R4 = 2kohm R 5-6-7 = 1kohm/3 = 333 ohm
Find R 3-4 and R 5-6-7.
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Online Resource for ETCH 213
Faculty: B. Allen
R2-3-4 = R2
R3-4/(R2 + R3-4) = 1k
2k/(1k + 2k) = 667ohm
Find R2-3-4
.
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Online Resource for ETCH 213
Faculty: B. Allen
RT = 1k +667ohm +333ohm = 2kohm
V1 = R1/RT VT = 1k/2k 12V = 6V
V2-3-4 = R2-3-4/RT 12V = 667/2k 12V = 4V
V5-6-7 = R5-6-7/RT 12V = 333/2k 12V = 2V
Find RT, V1, V2-3-4, V5-6-7.
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Online Resource for ETCH 213
Faculty: B. Allen
Voltage division in a series-
parallel circuit. SummaryFind:
V1 = 6V
V2 = 4V
V3 = 2V
V4 = 2V
V5 = 2V
V6 = 2V
V7 = 2V
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Online Resource for ETCH 213
Faculty: B. Allen
Branch current in a series-
parallel circuitFind:
I1
I2
I3
I4
I5
I6
I7
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Online Resource for ETCH 213
Faculty: B. Allen
Find total current
Since RT = 2kohm,
IT = VT/RT = 12V/2kohm = 6mA.
I1 = 6mA.
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Online Resource for ETCH 213
Faculty: B. Allen
Find I2
, I3
, I4
I2 = R2-3-4/R2 IT = 667ohm/1k 6mA = 4 mA
I3
= I4
= R2-3-4
/R3-4
IT
= 667ohm/2kohm 6mA = 2mA
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Online Resource for ETCH 213
Faculty: B. Allen
Find I5, I6, I7
I5 = R5-6-7/R5 IT = 330ohm/1kohm 6mA = 2mA
I6 = R5-6-7/R6 IT = 330ohm/1kohm 6mA = 2mA
I7 = R5-6-7/R7
IT = 330ohm/1kohm
6mA = 2mA
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Online Resource for ETCH 213
Faculty: B. Allen
Branch current in a series-
parallel circuit: SummaryFind:
I1 = 6mA
I2 = 4mA
I3 = 2mA
I4 = 2mA
I5 = 2mA
I6 = 2mA
I7 = 2mA
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Online Resource for ETCH 213
Faculty: B. Allen
Power in a series-parallel
circuitPT = P1 + P2 + P3 +
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Online Resource for ETCH 213
Faculty: B. Allen
Five-step procedure for series-
parallel circuit analysisStep 1: Determine the total resistance.
Step 2: Determine the total current.
Step 3: Determine the voltage across each series
resistor and each parallel combination of resistors.
Step 4: Determine the value of current through each
parallel resistor in every parallel combination.Step 5: Determine the total and individual power
dissipated by the circuit.
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Online Resource for ETCH 213
Faculty: B. Allen
Loading of voltage-divider
circuitsLoading The adding of a load to a source
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Online Resource for ETCH 213
Faculty: B. Allen
The Wheatstone bridge
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Online Resource for ETCH 213
Faculty: B. Allen
Balanced Wheatstone bridge
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Online Resource for ETCH 213
Faculty: B. Allen
Unbalanced Wheatstone bridge
When the voltmeter in a bridge circuit
does not read zero, the bridge isunbalanced.
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Online Resource for ETCH 213
Faculty: B. Allen
Determining an unknown
resistor using a bridge circuit
Using a bridge circuit with a variable
resistor, force the voltmeter to read zero.
This will balance the bridge and the value
of the variable resistor will equal the
value of the unknown resistor.
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Online Resource for ETCH 213
Faculty: B. Allen
R-2R ladder circuits
R-2R A network or circuit composed of a
sequence of L networks connected in tandem.This R-2R circuit is used in digital-to-analog
converters.
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Online Resource for ETCH 213
Faculty: B. Allen
Simplification of R2R ladder
circuit
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Online Resource for ETCH 213
Faculty: B. Allen
Troubleshooting series-parallel
circuitsAn open in a series component No current flow
An open in a parallel component Current
A short in a series component Current
A short in a parallel component Current
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Online Resource for ETCH 213
Faculty: B. Allen
Theorems for DC circuits
Superposition Theorem
Thevenins Theorem
Nortons Theorem
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Online Resource for ETCH 213
Faculty: B. Allen
Voltage and current sources
Voltage Source The circuit or device that
supplies voltage to a load circuit.
Current Source The circuit or device thatsupplies current to a load circuit.
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Online Resource for ETCH 213
Faculty: B. Allen
Superposition Theorem
In a network or circuit containing two or more voltage
sources, the current at any point is equal to the algebraic sumof the individual source currents produced by each source
acting separately.
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Online Resource for ETCH 213
Faculty: B. Allen
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Online Resource for ETCH 213
Faculty: B. Allen
Thevenins Theorem
Any network of voltage sources and resistors can be replaced
by a single equivalent voltage source (VTH) in series with asingle equivalent resistance (RTH).
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Online Resource for ETCH 213
Faculty: B. Allen
To Thevenize a circuit
Identify the circuit to be Thevenized.
Measure the voltage at the output. This is the VTH.
Remove the sources and replace them with a short;
measure the resistance at the output. This is the RTH.
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Online Resource for ETCH 213
Faculty: B. Allen
Find the Thevenin equivalent
circuit for:
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Online Resource for ETCH 213
Faculty: B. Allen
Thevenin equivalent circuit
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Online Resource for ETCH 213
Faculty: B. Allen
Find VTH
.
VTH = 1.33V
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Online Resource for ETCH 213
Faculty: B. Allen
Find RTH
.
RTH = 2kohm
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Online Resource for ETCH 213
Faculty: B. Allen
Nortons Theorem
Any network of voltage sources and
resistors can be replaced by a singleequivalent current source, IN, in parallel
with a single equivalent resistance, RN.
T fi d th i l t N t
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Online Resource for ETCH 213
Faculty: B. Allen
To find the equivalent Norton
circuitIdentify the circuit for a Norton equivalent circuit.
Measure the the short circuit amperes. This is IN.
Replace the sources with shorts and measure the
resistance at the output. This is RN.
Fi d th N t i l t
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Online Resource for ETCH 213
Faculty: B. Allen
Find the Norton equivalent
circuit for:
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Online Resource for ETCH 213
Faculty: B. Allen
Norton equivalent circuit
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Online Resource for ETCH 213
Faculty: B. Allen
Find IN
.
IN
= -2.333mA
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Online Resource for ETCH 213
Faculty: B. Allen
Find RN.
RN = 2.0kohm
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Online Resource for ETCH 213
End ofIntroduction to Series-Parallel DC
Circuits