Introduction to Series-Parallel DC Circuits - Cuesta

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7 Οκτ 2013 (πριν από 3 χρόνια και 10 μήνες)

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Online Resource for ETCH 213
Faculty: B. Allen
Introduction to Series-Parallel DC Circuits
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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Faculty: B. Allen
Series-parallel resistive circuits
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Tracking current through a
series-parallel circuit
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Faculty: B. Allen
Total resistance in a series-
parallel circuit
Step 1: Determine the equivalent resistance of all
branch series-connected resistors.
Step 2: Determine the equivalent resistance of all
parallel-connected combinations.
Step 3: Determine the equivalent resistance of the
remaining series-connected resistors.
Online Resource for ETCH 213
Faculty: B. Allen
Calculating total resistance
Find the equivalent resistance for R5
and R6.
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Find the equivalent resistance for R4
and R5-6.
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Faculty: B. Allen
Find the equivalent resistance for R2, R3, and R4-5-6.
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Faculty: B. Allen
Find RT.
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Faculty: B. Allen
Voltage division in a series-
parallel circuit
Find:
V1
V2
V3
V4
V5
V6
V7
Online Resource for ETCH 213
Faculty: B. Allen
R3-4
= R3
+ R4
= 2kohmR
5-6-7
= 1kohm/3 = 333 ohm
Find R 3-4
and R 5-6-7.
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.
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.
Online Resource for ETCH 213
Faculty: B. Allen
Voltage division in a series-
parallel circuit. Summary
Find:
V1 = 6V
V2 = 4V
V3 = 2V
V4 = 2V
V5 = 2V
V6 = 2V
V7 = 2V
Online Resource for ETCH 213
Faculty: B. Allen
Branch current in a series-
parallel circuit
Find:
I1
I2
I3
I4
I5
I6
I7
Online Resource for ETCH 213
Faculty: B. Allen
Find total current
Since RT
= 2kohm,
IT
= VT/RT
= 12V/2kohm = 6mA.
I1
= 6mA.
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
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
Online Resource for ETCH 213
Faculty: B. Allen
Branch current in a series-
parallel circuit: Summary
Find:
I1 = 6mA
I2 = 4mA
I3 = 2mA
I4 = 2mA
I5 = 2mA
I6 = 2mA
I7 = 2mA
Online Resource for ETCH 213
Faculty: B. Allen
Power in a series-parallel
circuit
PT
= P1
+ P2
+ P3
+ …
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Faculty: B. Allen
Five-step procedure for series-
parallel circuit analysis
Step 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.
Online Resource for ETCH 213
Faculty: B. Allen
Loading of voltage-divider
circuits
Loading –The adding of a load to a source
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The Wheatstone bridge
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Balanced Wheatstone bridge
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Unbalanced Wheatstone bridge
When the voltmeter in a bridge circuit
does not read zero, the bridge is
unbalanced.
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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.
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.
Online Resource for ETCH 213
Faculty: B. Allen
Simplification of R–2R ladder
circuit
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Faculty: B. Allen
Troubleshooting series-parallel
circuits
An 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
Online Resource for ETCH 213
Faculty: B. Allen
Theorems for DC circuits
Superposition Theorem
Thevenin’sTheorem
Norton’s Theorem
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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 that
supplies current
to a load circuit.
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 sum
of the individual source currents produced by each source
acting separately.
Online Resource for ETCH 213
Faculty: B. Allen
Online Resource for ETCH 213
Faculty: B. Allen
Thevenin’sTheorem
Any network of voltage sources and resistors can be replaced
by a single equivalent voltage source (VTH) in series with a
single equivalent resistance (RTH).
Online Resource for ETCH 213
Faculty: B. Allen
To Thevenizea 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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Faculty: B. Allen
Find the Theveninequivalent
circuit for:
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Theveninequivalent circuit
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Find VTH.
VTH
= 1.33V
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Find RTH.
RTH
= 2kohm
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Norton’s Theorem
Any network of voltage sources and
resistors can be replaced by a single
equivalent current source, IN, in parallel
with a single equivalent resistance, RN.
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Faculty: B. Allen
To find the equivalent Norton
circuit
Identify 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.
Online Resource for ETCH 213
Faculty: B. Allen
Find the Norton equivalent
circuit for:
Online Resource for ETCH 213
Faculty: B. Allen
Norton equivalent circuit
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Faculty: B. Allen
Find IN.
IN
= -2.333mA
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Find RN.
RN
= 2.0kohm
Online Resource for ETCH 213
Faculty: B. Allen
End of
Introduction to Series-Parallel DC
Circuits