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ELECTRICITY & MAGNETISM
LECTURE # 7
BY
MOEEN GHIYAS
(Series – Parallel Networks – Chapter 7)
Introductory Circuit Analysis by Boylested (10th Edition)
TODAY’S LESSON
Today’s Lesson Contents
• Introduction – Series-Parallel Networks
• General Approach
• Reduce and Return Approach
• Ladder Networks
• Voltage Divider Supply (Loaded and Unloaded)
• Potentiometer Loading
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.
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.
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
General Approach
• Apply KCL at node a
Reduce and Return Approach
• Used with single-source
(or multi-sources
connected only in simple
series or parallel) seriesparallel networks.
• In this analytical approach
we first reduce network
towards the source.
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.
Reduce and Return Approach
• Then find the desired
unknowns by expanding
the circuit back to original
network.
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)
Ladder Network
Ladder Network
By Current Divider law
By Ohm’s Law
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.
Voltage Divider Supply (Loaded & Unloaded)
• The application of a load can affect the
terminal voltage of the supply.
1k Ω
1k Ω
1k Ω
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 Ω
1k Ω
1k Ω
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.
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.
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 .
Voltage Divider Supply (Loaded & Unloaded)
• Applying voltage divider law
versus 100 V under no-load conditions
Voltage Divider Supply (Loaded & Unloaded)
• Applying voltage divider law
versus 60 V under no-load conditions
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 Ω
1k Ω
1k Ω
Voltage Divider Supply (Loaded & Unloaded)
• Comparing current levels
• With 20Ω load
• With 1kΩ
1k Ω
1k Ω
1k Ω
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
can be used
Voltage Divider Supply (Loaded & Unloaded)
• For R1:
Apply KCL at node a,
• Note: Va ≠ VR1
• But VR1 = Vab
Yes! 2W resistor can be used
Voltage Divider Supply (Loaded & Unloaded)
• For R2:
Apply KCL at node b,
Yes! 2W resistor
can be used
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.
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.
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:
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
to the expected level of 1 V.
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.
1/10 of source voltage E = 10V
Summary / Conclusion
• Introduction – Series-Parallel Networks
• General Approach
• Reduce and Return Approach
• Ladder Networks
• Voltage Divider Supply (Loaded and Unloaded)
• Potentiometer Loading