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Lecture 4 (Week 4)
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Series - Parallel CircuitsOEk 1115 - Fundamentals of Electronics
Lecture 4
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OutlineSeries-Parallel Circuits
Total Resistance
Total Current
Branch Currents
Voltage Relationships
Load Current and Bleeder Current
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Series - Parallel CircuitsA series-parallel circuit consists of combinations of both series and parallel
current paths.
It is important to be able to identify how the components in a circuit are arranged
in terms of their series and parallel relationships.
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Series - Parallel Circuits5.
Series - Parallel Circuits6.
Series - Parallel Circuits7.
Series - Parallel CircuitsExample. Identify the series-parallel relationships.
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Series - Parallel CircuitsSolution.
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Series - Parallel CircuitsExample. Describe the series-parallel combination between terminals A and D.
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Series - Parallel CircuitsSolution.
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Series - Parallel CircuitsExample. Describe the total resistance between each pair of terminals.
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Series - Parallel CircuitsSolution.
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Series - Parallel CircuitsExample. Identify the series-parallel relationships.
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Series - Parallel CircuitsSolution.
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Analysis of Series-Parallel Resistive CircuitsThe analysis of series-parallel circuits can be approached in many ways,
depending on what information you need and what circuit values you know.
If you know Ohm’s law, Kirchhoff’s laws, the voltage-divider formula, and the
current-divider formula, and if you know how to apply these laws, you can solve
most resistive circuit analysis problems.
The ability to recognize series and parallel combinations is, of course, essential.
There is no standard “cookbook” approach that can be applied to all situations.
Logical thought is the most powerful tool you can apply to problem solving.
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Total ResistanceTo find the total resistance (RT) of a series-parallel combination,
1. identify the series and parallel relationships,
2. determine total series and total parallel resistance.
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Total ResistanceExample. Determine RT between terminals A and B of the circuit.
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Total ResistanceSolution.
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Total ResistanceExample. Find RT of the circuit.
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Total ResistanceSolution.
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Total CurrentOnce you know the total resistance and the source voltage, you can apply Ohm’s
law to find the total current in a circuit.
Example. Let’s find the total current in the circuit in last example. Assume that the
source voltage is 10 V. The calculation is
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Branch CurrentsUsing the current-divider formula, Kirchhoff’s current law, Ohm’s law, or
combinations of these, you can find the current in any branch of a series-parallel
circuit.
In some cases, it may take repeated application of the formula to find a given
current.
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Branch CurrentsExample. Determine the current through R4 if Vs = 5 V.
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Branch CurrentsSolution.
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Voltage Relationships26.
Voltage Relationships1. V(R1) and V(R2) are equal because R1 and R2 are in parallel.
2. V(R3) is equal to V(R4) + V(R5) because R3 is in parallel with the series
combination of R4 and R5.
3. V(R4) is about one-third of the voltage from B to C because R4 is about onethird of the resistance R4 + R5 (by the voltage-divider principle).
4. V(R5) is about two-thirds of the voltage from B to C because R5 is about twothirds of R4 + R5.
5. V(R1) + V(R3) - Vs = 0 because, by Kirchhoff’s voltage law, the algebraic sum
of the voltage drops around a single closed path must equal zero.
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Voltage RelationshipsExample. Verify that the voltmeter readings in previous slide are correct. The
circuit is redrawn as a schematic.
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Solution.29.
Voltage RelationshipsDetermine the voltage drop across each resistor in Figure
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Voltage Dividers with Resistive LoadsThe voltage divider in circuit produces an output voltage (Vout). This voltage is the
unloaded output voltage.
When a load resistor, RL is connected from the output to ground the output voltage
is reduced by an amount that depends on the value of RL. This effect is called
loading.
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Voltage Dividers with Resistive LoadsExample.
a) Determine the unloaded output voltage of the voltage divider.
b) Find the loaded output voltages of the voltage divider for the following two
values of load resistance: RL = 10 kOhm and RL = 100 kOhm.
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Solution.33.
Load Current and Bleeder CurrentIn a multiple-tap loaded voltage-divider circuit, the total current drawn from the
source consists of currents through the load resistors, called load currents, and
the divider resistors.
Bleeder current is a current left after the total load current is subtracted from the
total current in the circuit.
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Voltage Dividers with Resistive LoadsExample. Determine the load currents I(RL1)and and I(RL2) and the bleeder
current I3 in the two-tap loaded voltage divider.
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Voltage Dividers with Resistive LoadsSolution.
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Voltage Dividers with Resistive LoadsSolution.
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Voltage Dividers with Resistive LoadsSolution.
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Serial and ParallelFind the total resistance between A and B in the circuit, current through R3, VR2,
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Serial and ParallelDetermine total resistance and total current in the circuit
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Serial and ParallelDetermine the total resistance and the voltage at points A, B, and C in the circuit
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Serial and ParallelDetermine the voltage at point A and B in the circuit
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Q&AAny Questions?