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ELECTRICITY & MAGNETISM
LECTURE # 7
BY
MOEEN GHIYAS
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TODAY’S LESSON
(Series – Parallel Networks – Chapter 7)
Introductory Circuit Analysis by Boylested (10th Edition)
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Today’s Lesson Contents
• Introduction – Series-Parallel Networks
• General Approach
• Reduce and Return Approach
• Ladder Networks
• Voltage Divider Supply (Loaded and Unloaded)
• Potentiometer Loading
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Introduction – Series-Parallel Networks
• Series-parallel networks are networks that contain both
series and parallel circuit configurations.
• A firm understanding of the basic principles is sufficient
to begin an investigation of any single-source dc (or
multi-sources connected only in simple series or
parallel) network having a combination of series and
parallel elements or branches.
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General Approach
• Take a moment to study the problem “in total” and make
a brief mental sketch of the overall approach.
• Next examine each region of the network independently
before tying them together in series-parallel
combinations
• Redraw the network as often as possible with the
reduced branches towards source keeping unknown
quantities undisturbed or have provision for the trip back
to unknown quantities from the source.
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General Approach
• Example – For the network of fig, determine the voltages V1
and V2 and the current I.
• Solution:
• Redraw the circuit
• By observation
• . By KVL in right loop
• . or
• . or
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General Approach
• Apply KCL at node a
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Reduce and Return Approach
• Used with single-source
(or multi-sources
connected only in simple
series or parallel) series-
parallel networks.
• In this analytical approach
we first reduce network
towards the source.
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Reduce and Return Approach
• Reduce network to single
element (RT) towards the
source to determine the
source current (IS).
• Followed by expanding the
circuit backwards.
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Reduce and Return Approach
• Then find the desired
unknowns by expanding
the circuit back to original
network.
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Ladder Network
• Ladder network appears in fig. The reason for the
terminology is quite obvious for the repetitive structure
• Applying reduce and return approach (starting farthest
from source)
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Ladder Network
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Ladder Network
By Current Divider law
By Ohm’s Law
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Voltage Divider Supply (Loaded & Unloaded)
• Through a voltage divider network such as
the one in fig, a number of terminal voltages
can be made available from a single supply.
• The voltage levels shown (with respect to
ground) are determined by a direct
application of the voltage divider rule.
• Figure reflects a no load situation due to the
absence of any current-drawing elements
connected between terminals a, b, or c and
ground.
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Voltage Divider Supply (Loaded & Unloaded)
• The application of a load can affect the
terminal voltage of the supply.
1k 1k ΩΩ
1k 1k ΩΩ
1k 1k ΩΩ
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Voltage Divider Supply (Loaded & Unloaded)
• The larger the resistance level of the applied loads
compared to the resistance level of the voltage divider
network, the lower the current demand from a supply,
closer the terminal characteristics are to the no-load
levels.
1k 1k ΩΩ
1k 1k ΩΩ
1k 1k ΩΩ
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Voltage Divider Supply (Loaded & Unloaded)
• Let us consider the network of fig with resistive loads
that are the average value of the resistive elements of
the voltage divider network.
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Voltage Divider Supply (Loaded & Unloaded)
• The voltage Va is unaffected by the load RL1 since the
load is in parallel with the supply voltage E.
• Thus Va = 120 V, same as the no-load level.
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Voltage Divider Supply (Loaded & Unloaded)
• Now remaining load situation create a series-parallel effect
• R′3 = R3 || RL3 = 30 Ω || 20 Ω =12 Ω .
• R′2 = (R2 + R′3) || RL2 = 32Ω || 20Ω = 12.31Ω .
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Voltage Divider Supply (Loaded & Unloaded)
• Applying voltage divider law
versus 100 V under no-load
conditions
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Voltage Divider Supply (Loaded & Unloaded)
• Applying voltage divider law
versus 60 V under no-load
conditions
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Voltage Divider Supply (Loaded & Unloaded)
• If the load resistors are changed to the 1kΩ level, the terminal
voltages will all be relatively close to the no-load values
1k 1k ΩΩ
1k 1k ΩΩ
1k 1k ΩΩ
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Voltage Divider Supply (Loaded & Unloaded)
• Comparing current levels
• With 20Ω load
• With 1kΩ
1k 1k ΩΩ
1k 1k ΩΩ
1k 1k ΩΩ
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Voltage Divider Supply (Loaded & Unloaded)
• Example – Determine R1, R2, and R3 for the voltage divider
supply of fig. Can 2W resistors be used in the design?
• Solution: For R3:
Yes! 2W resistor Yes! 2W resistor
can be usedcan be used
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Voltage Divider Supply (Loaded & Unloaded)
• For R1: Apply KCL at node a,
• Note: Va ≠ VR1
• But VR1 = Vab
Yes! 2W resistor can be usedYes! 2W resistor can be used
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Voltage Divider Supply (Loaded & Unloaded)
• For R2: Apply KCL at node b,
Yes! 2W resistor Yes! 2W resistor
can be usedcan be used
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Potentiometer Loading
• For the unloaded potentiometer of fig, the output
voltage is determined by the voltage divider rule, with
RT in the figure representing the total resistance of the
potentiometer.
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Potentiometer Loading
• When a load is applied as shown in fig (right), the output
voltage VL is now a function of the magnitude of the load
applied since R1 is not as shown in fig (left) but is instead the
parallel combination of R1 and RL.
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Potentiometer Loading
• If it is desired to have good control of output voltage VL
through the controlling dial or knob (Design Parameter),
it is advisable to choose a load or potentiometer that
satisfies the following relationship:
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Potentiometer Loading
• For example, if we disregard eq. and choose
a 1MΩ potentiometer with a 100Ω load and set the wiper
arm to 1/10 of total resistance, as shown, then
which is extremely small compared which is extremely small compared
to the expected level of 1 V.to the expected level of 1 V.
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Potentiometer Loading
• Using the reverse situation of RT = 100Ω and RL = 1 MΩ and
the wiper arm at the 1/10 position, as in fig, we find
which is the desired voltage i.e. which is the desired voltage i.e.
1/10 of source voltage E = 10V1/10 of source voltage E = 10V
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Summary / Conclusion
• Introduction – Series-Parallel Networks
• General Approach
• Reduce and Return Approach
• Ladder Networks
• Voltage Divider Supply (Loaded and Unloaded)
• Potentiometer Loading
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