lecture7 series and parallel

7/30/2019 Lecture7 Series and Parallel

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Online Resource for ETCH 213

Faculty: B. Allen

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 series-

parallel circuitStep 1: Determine the equivalent resistance of all

branch series-connected resistors.

Step 2: Determine the equivalent resistance of allparallel-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 series-

parallel circuitFind:

V1

V2

V3

V4

V5

V6

V7


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R3-4 = R3 + R4 = 2kohm R 5-6-7 = 1kohm/3 = 333 ohm

Find R 3-4 and R 5-6-7.


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R2-3-4 = R2

R3-4/(R2 + R3-4) = 1k

2k/(1k + 2k) = 667ohm

Find R2-3-4

.


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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

Find RT, V1, V2-3-4, V5-6-7.


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Faculty: B. Allen

Voltage division in a series-

parallel circuit. SummaryFind:

V1 = 6V

V2 = 4V

V3 = 2V

V4 = 2V

V5 = 2V

V6 = 2V

V7 = 2V


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Faculty: B. Allen

Branch current in a series-

parallel circuitFind:

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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Faculty: B. Allen

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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Faculty: B. Allen

Branch current in a series-

parallel circuit: SummaryFind:

I1 = 6mA

I2 = 4mA

I3 = 2mA

I4 = 2mA

I5 = 2mA

I6 = 2mA

I7 = 2mA


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Power in a series-parallel

circuitPT = P1 + P2 + P3 +


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Five-step procedure for series-

parallel circuit analysisStep 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

circuitsLoading 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 isunbalanced.


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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 R2R ladder

circuit


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Troubleshooting series-parallel

circuitsAn 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

Thevenins Theorem

Nortons 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 thatsupplies 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 sumof the individual source currents produced by each source

acting separately.


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Thevenins Theorem

Any network of voltage sources and resistors can be replaced

by a single equivalent voltage source (VTH) in series with asingle 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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Nortons Theorem

Any network of voltage sources and

resistors can be replaced by a singleequivalent current source, IN, in parallel

with a single equivalent resistance, RN.

T fi d th i l t N t


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To find the equivalent Norton

circuitIdentify 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.

Fi d th N t i l t


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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 ofIntroduction to Series-Parallel DC

Circuits

lecture7 series and parallel

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