Chapter 7
The Series-Parallel
Network
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Branch |
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Part of a circuit that can be
simplified into two terminals |
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Components between these two terminals |
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Resistors, voltage sources, or other
elements |
The Series-Parallel
Network
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Complex circuits |
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May be separated both series and/or
parallel elements |
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Other circuits |
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Combinations which are neither series
nor parallel |
The Series-Parallel
Network
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To analyze a circuit |
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Identify elements in series and
elements in parallel |
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In this circuit |
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R2, R3, and R4
are in parallel |
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This parallel combination |
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Series with R1 and R5 |
The Series-Parallel
Network
The Series-Parallel
Network
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In this circuit |
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R3 and R4 are in
parallel |
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Combination is in series with R2 |
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Entire combination is in parallel with R1 |
Analysis of
Series-Parallel Circuits
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Rules for analyzing series and parallel
circuits still apply |
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Same current occurs through all series
elements |
Analysis of
Series-Parallel Circuits
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Same voltage occurs across all parallel
elements |
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KVL and KCL apply for all circuits |
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Whether they are series, parallel, or
series-parallel |
Analysis of
Series-Parallel Circuits
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Redraw complicated circuits showing the
source at the left-hand side |
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Label all nodes |
Analysis of
Series-Parallel Circuits
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Develop a strategy |
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Best to begin analysis with components
most distant from the source |
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Simplify recognizable combinations of
components |
Analysis of
Series-Parallel Circuits
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Determine equivalent resistance RT |
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Solve for the total current |
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Label polarities of voltage drops on
all components |
Analysis of
Series-Parallel Circuits
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Calculate how currents and voltages
split between elements in a circuit |
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Verify your answer by taking a
different approach (when feasible) |
Analysis of
Series-Parallel Circuits
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Combining R2 and R3
in parallel |
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Circuit reduces to a series circuit |
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Use Voltage Divider Rule to determine Vab
and Vbc. |
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Note that Vbc = V2
is the voltage across R2 and R3 |
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Calculate all currents from Ohm’s Law. |
Analysis of
Series-Parallel Circuits
Analysis of
Series-Parallel Circuits
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To find voltage Vab, |
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Redraw circuit in simple form |
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Original circuit |
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Two parallel branches |
Analysis of
Series-Parallel Circuits
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Vab |
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Determined by combination of voltages
across R1 and R2 , or R3 and R4 |
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Use Voltage Divider Rule to find two
voltages |
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Use KVL to find Vab |
Analysis of
Series-Parallel Circuits
Analysis of
Series-Parallel Circuits
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To find currents in the circuit |
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First redraw the circuit |
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Move source branch all the way to left |
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Reduce circuit to a series circuit |
Analysis of
Series-Parallel Circuits
Analysis of
Series-Parallel Circuits
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Voltages |
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Use Ohm’s Law or Voltage Divider Rule |
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Currents |
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Use Ohm’s Law or Current Divider Rule |
Analysis of
Series-Parallel Circuits
Bridge Circuit
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Circuit has Rx = 15 kW |
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Determine Vab |
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Redraw circuit as shown on slide |
Bridge Circuit
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Voltage Divider Rule |
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Determine Va and Vb. |
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Ground reference point |
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Take at bottom of circuit |
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Vab = 0.5 V |
Bridge Circuit
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Rx is a short circuit (0 W) |
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Voltage Divider Rule |
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Determine VR1 |
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VR2 = 10 V |
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Vab = 8 V |
Bridge Circuit
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Rx is open |
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Find VR1 |
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We know VR2 = 0 V |
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No current through it |
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Vab = –2 V |
Transistor Circuit
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Transistor |
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Device that amplifies a signal |
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Operating point of a transistor circuit |
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Determined by a dc voltage source |
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We will determine some dc voltages and
currents |
Transistor Circuit
Transistor Circuit
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Apply KVL: |
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VBB = RBIB
+ VBE + REIE |
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Using IE = 100IB,
we find IB = 14.3 mA. |
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Other voltages and currents can be
determined |
Potentiometers
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Example of variable resistor used as
potentiometer |
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Volume control on a receiver |
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Moveable terminal is at uppermost
position |
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Vbc = 60 V |
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At the lowermost position |
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Vbc = 0 V |
Potentiometers
Potentiometers
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Vbc changes |
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If load is added to circuit |
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At upper position |
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Vbc = 40 V |
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At the lower position |
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Vbc = 0 V |