1 electronics parallel resistive circuits part 1 copyright © texas education agency, 2014. all...

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Electronics

ParallelResistive

CircuitsPart 1

Copyright © Texas Education Agency, 2014. All rights reserved.

What is a Parallel Circuit?

A parallel circuit is a circuit with more than one path for current flow

This type of circuit is very common This is the type of circuit that is used to deliver

power to an outlet in your home Circuit analysis in a parallel circuit starts the

same way as a series circuit—with Kirchhoff’s Laws

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Review of Kirchhoff’s Law’s

Voltage law- the sum of all voltages in a closed loop is equal to zero The sum of the voltage drops equals the sum of the

voltage sources All of the voltage is always used in a loop

Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node The current into a conductor is the same as the

current out of the conductorCopyright © Texas Education Agency, 2014. All rights reserved.

The Simplest Parallel Circuit

Here is an example of the simplest parallel circuit

This circuit has a power supply and two paths for current flow

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The Simplest Parallel Circuit

The two resistors are different loads

Load one is labeled R1 and load two is labeled R25

R1 R2VS


Paths for Current Flow

Path One

6

R1 R2VS



Path Two

7

R1 R2VS



Path Two

Now let’s apply Kirchhoff’s Voltage Law to each path

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R1 R2VS


Voltage in Parallel Circuits

Path One- place polarities for the two components

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R1 R2VS


Kirchhoff’s Law in Parallel Circuits

Path One- place polarities for the two components

In a path for current flow from one side of the battery to the other, the sum of the voltage in a closed loop equals zero

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R1 R2VS



Path One- start from the top of the battery, and read polarities going into each component

+ VS – VR1 = 0 or VS = VR1

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R1 R2VS



Path Two

+ VS – VR2 = 0 or VS = VR2

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R1 R2VS


Voltage in Parallel Circuits

This is the first equation for a parallel circuit

This equation says that the voltage in each parallel path is the same

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R1 R2


VS = VR1 = VR2

VS

Current in a Parallel Circuit

Both paths exist at the same time The current that flows through R1 does not

flow through R2

The current that flows through R2 does not flow through R1

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R1 R2


VS


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R1 R2VS


Each current is separate and independent To calculate each current flow, use Ohm’s Law

I1 = I2 =


I1 = , I2 = Apply Kirchhoff’s Current Law to this circuit

Current law- the sum of the currents into a node is equal to the sum of the currents leaving the node

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R1 R2VS


A node is where current splits or combines It is a junction or branching point for current

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R1 R2


VS


A node is where current splits or combines It is a junction or branching point for current

Here are the nodes

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R1 R2


VS


Current combines or comes back together here

Current splits apart here

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R1 R2


VS

Water Flow Equivalent

Here is a picture showing the same effect using water flow in a pipe

Water flow here is the same as water flow here

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Flow splits into two parts here

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These two points are the equivalent of an electrical node or junction Where flow splits and then comes back together

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There are actually three different currents

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R1 R2


VS


There are actually three different currents Here is I1

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R1 R2


VS


There are actually three different currents Here is I1

Here is I225

R1 R2


VS


Here is IT (total current)

IT is the current leaving and entering the battery 26

R1 R2


VS


Here is the picture using current flow symbols

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IT ITI2



From Kirchhoff’s Current Law

IT = I1 + I2

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R1 R2IT


VS


From Kirchhoff’s Current Law

This is the second parallel circuit equation

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R1 R2IT


IT = I1 + I2VS

Start with the equation for parallel circuit current

Using Ohm’s Law, substitute for current I = so

Recall the voltage rule in a parallel circuit

Substitute this rule into the previous equation

Resistance in a Parallel Circuit

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IT = I1 + I2

VS = VR1 = VR2


IT = , I1 = , I2 = = +

Resistance in a Parallel Circuit

After substitution

VS is the same in each term so it divides out, giving us the following formula for resistance in a parallel circuit

This is the third parallel circuit equation

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= +

Parallel Circuit Equations

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IT = I1 + I2 VS = VR1 = VR2


For two resistors


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(current adds)

(voltage is the same)

(resistance is more complex,but it basically divides)


IT = I1 + I2 VS = VR1 = VR2


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(current adds)

(voltage is the same)

(resistance is more complex,but it basically divides)


These three formulas (plus Ohm’s Law)form a “tool kit” to analyze parallel circuits.

IT = I1 + I2 VS = VR1 = VR2

Understanding Resistance in a Parallel Circuit

Resistance looks a little more complicated, so let’s examine it more closely

Consider the following circuit

Each switch is open; each light is off

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S1 S2 S3

L1 L2 L3


VS


Close S1 and L1 comes on We get current I1 from the battery Each light is identical

Total current = I1 , total resistance = R136

VSS1 S2 S3

L1 L2 L3



Next close S2 and L2 comes on We get additional current I2 from the battery Total current = I1 + I2, double the current

This means total resistance must be cut in half compared to the previous circuit

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S1 S2 S3

L1 L2 L3


VS

Do the Math

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Use the following formula

Assume R1 = R2 = 30 Ω

= = .0333 + .0333 = 15 Ω

Example Problem 1

For the following circuit, calculate RT and IT

Begin by writing down the equations we need Start with the formula for RT. Once we calculate

that, we can solve for IT 39


R1 =300 Ω R2 =200 Ω VS =15 V

Example Problem 1

For the following circuit, calculate RT and IT

Begin by writing down the equations we need40


R1 =300 Ω R2 =200 Ω VS =15 V

and IT =

Example Problem 1

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=

Example Problem 1

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= 0.00333 + 0.005 = 0.00833 =

=

Example Problem 1

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RT = 120 Ω = 0.00333 + 0.005 = 0.00833

= =

Example Problem 1

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RT = 120 Ω = 0.00333 + 0.005 = 0.00833

= =

IT = =

Example Problem 1

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RT = 120 Ω = 0.00333 + 0.005 = 0.00833

= =

IT = = = .125 A

1 electronics parallel resistive circuits part 1 copyright © texas education agency, 2014. all...

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