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Introduction to Series-Parallel DC Circuits
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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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Series-parallel resistive circuits
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Tracking current through a
series-parallel circuit
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Total resistance in a seriesparallel 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.
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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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Find the equivalent resistance for R2, R3, and R4-5-6.
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Find RT.
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Voltage division in a seriesparallel circuit
Find:
V1
V2
V3
V4
V5
V6
V7
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Find R 3-4 and R 5-6-7.
R3-4 = R3 + R4 = 2kohm
R5-6-7 = 1kohm/3 = 333 ohm
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Find R2-3-4.
R2-3-4 = R2 × R3-4/(R2 + R3-4) = 1k × 2k/(1k + 2k) = 667ohm
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Find RT, V1, V2-3-4, V5-6-7.
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
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Voltage division in a seriesparallel circuit. Summary
Find:
V1 = 6V
V2 = 4V
V3 = 2V
V4 = 2V
V5 = 2V
V6 = 2V
V7 = 2V
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Branch current in a seriesparallel circuit
Find:
I1
I2
I3
I4
I5
I6
I7
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Find total current
Since RT = 2kohm,
IT = VT/RT = 12V/2kohm = 6mA.
I1 = 6mA.
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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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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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Branch current in a seriesparallel circuit: Summary
Find:
I1 = 6mA
I2 = 4mA
I3 = 2mA
I4 = 2mA
I5 = 2mA
I6 = 2mA
I7 = 2mA
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Power in a series-parallel
circuit
PT = P1 + P2 + P3 + …
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Five-step procedure for seriesparallel 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.
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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.
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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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Simplification of R–2R ladder
circuit
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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
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Theorems for DC circuits
Superposition Theorem
Thevenin’s Theorem
Norton’s Theorem
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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.
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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.
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Thevenin’s Theorem
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).
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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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Find the Thevenin equivalent
circuit for:
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Thevenin equivalent 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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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.
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Find the Norton equivalent
circuit for:
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Norton equivalent circuit
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Find IN.
IN = -2.333mA
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Find RN.
RN = 2.0kohm
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End of
Introduction to Series-Parallel DC
Circuits
Online Resource for ETCH 213
Faculty: B. Allen