1 Electronics Parallel Resistive Circuits Part 2 Copyright © Texas Education Agency, 2014. All rights reserved

1

Electronics

ParallelResistive

CircuitsPart 2

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

More Complex Parallel Circuits

Let’s do a parallel circuit analysis with three branches

Follow the same analysis process as before

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VS R1 R2 R3



3

R1 R2 R3I1


VS

Path 1 has current I1 Apply Kirchhoff’s Law to this current loop + VS – VR1 = 0 or

VS = VR1 , so from Ohm’s Law


4

R1 R2 R3I2


VS




5

R1 R2 R3I3


VS



Parallel Circuit Equations

6

IT = I1 + I2 + I3 VS = VR1 = VR2 = VR3


+


7

IT = I1 + I2 + I3 VS = VR1 = VR2 = VR3 (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

+

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 = R19

VSS1 S2 S3

L1 L2 L3



Next close S2 and S3, L2 and L3 come on We get additional current I2 ,I3 from the battery Total current = I1 + I2 + I3, triple the current

This means total resistance must be cut to one third

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S1 S2 S3

L1 L2 L3


VS

Use the following formula:

Assume R1 = R2 = R3 = 30 Ω

or

Do the Math

11


+ + + +

.1 RT = 10 Ω

An Easier Way

Now lets look at an easier way to calculate total resistance

Use the button on your calculator On some calculators it will be a button This button does the hard part of the math for

you by calculating the inverse of a value Let’s try using this button on the previous

example

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Let’s try this first with two resistors

Using the TI-83 buttons, perform the following

Calculating Total Resistance

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3 0 + 3 0 ENTER ENTER


=

Let’s try this first with two resistors


If you did it right, 15 will be displayed You only enter resistance values and calculator

functions


14

3 0 + 3 0 ENTER ENTER


=

Now try it for a circuit with three resistors



15

3 0 + 3 0

ENTER

+

3 0 ENTER


+ + +

Now try it for a circuit with three resistors


If you did it right, 10 will be displayed


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3 0 + 3 0

ENTER

+

3 0 ENTER


+ + +

Example Problem 1

For the following circuit, calculate RT and IT

Begin by writing down the equations we need17


R1 =300 Ω R2 =200 Ω VS =15 V

and IT =

Example Problem 1

18


3 0 + 2 0

ENTER ENTER

0 0

=

Example Problem 1

19


3 0 + 2 0

ENTER ENTER

0 0

RT = 120 Ω

=

Example Problem 1

20


3 0 + 2 0

ENTER ENTER

0 0

RT = 120 Ω

=

IT = = 0.125 A

Example Problem 2

For the following circuit, calculate RT and IT

Begin by writing down the equations we need

We have enough information to solve these21


VS =14.5 V R1 =1.4 kΩ R2 =2.2 kΩ R3 =1.8 kΩ

and + IT =

Example Problem 2

22


+ + +

Example Problem 2

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RT = 580 Ω + + +

Example Problem 2

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RT = 580 Ω + + +

IT = = =

Example Problem 2

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RT = 580 Ω + + +

IT = = = 0.025 AIT = 25 mA

Example Problem 3

For the following circuit, calculate VS

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R1 =330 Ω R2 =560 Ω VS = ?IT = 106 mA

Example Problem 3


Write the equation that solves the problem

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R1 =330 Ω R2 =560 Ω VS = ?IT = 106 mA

VS = VT = IT • RT

Example Problem 3


Write the equation that solves the problem

Look for what is needed to solve this equation We have IT, we need RT

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R1 =330 Ω R2 =560 Ω VS = ?IT = 106 mA

VS = VT = IT • RT

Example 3 Solution

Write the equation for RT

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=

Example 3 Solution


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RT = 207.6 Ω =

Example 3 Solution


Plug this value into the first equation

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RT = 207.6 Ω =

VS = VT = IT • RT = .106 A • 207.6 Ω

Example 3 Solution


Plug this value into the first equation

32


RT = 207.6 ΩVS = VT = IT • RT = .106 A • 207.6 ΩVS = 22 V

=

Example Problem 4

Calculate R1

33


R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mAVS =20 V

IT = 18 mA

Example Problem 4

Calculate R1

Write the formula for R134


R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mA

IT = 18 mAVS =20 V

Example Problem 4

Calculate R1

Write the formula for R1 Now we need a formula that solves for I1 35


R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mA

IT = 18 mA

= V SI 1

VS =20 V

Example Problem 4

Calculate R1

Write the formula for R1 Now we need a formula that solves for I1

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R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mA

IT = 18 mA

IT = I1 + I2

V SI 1

VS =20 V

=

Problem 4 Solution

To calculate I1, or

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R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mAVS =20 V

IT = 18 mAIT = I1 + I2 I1 = IT – I2

I1 = 18 mA – 10 mA = 8 mA

Problem 4 Solution

To calculate I1, or

Plug into first formula

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R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mA

IT = 18 mAIT = I1 + I2 I1 = IT – I2

I1 = 18 mA – 10 mA = 8 mAVS =20 V

= =

Problem 4 Solution

To calculate I1, or

Plug into first formula

39


R1 =? Ω I1 = ?R2 =? Ω I2 = 10 mAVS =20 V

IT = 18 mAIT = I1 + I2 I1 = IT – I2

I1 = 18 mA – 10 mA = 8 mA = = 2.5 kΩ

Example Problem 5

For the following circuit calculate R1

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R1 =? Ω R2 =26 kΩ VS =38 VIT = 3.36 mA

Example Problem 5


Write the equation that solves the problem Note: there is more than one equation for R1

Look for what is needed to solve this equation

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R1 =? Ω R2 =26 kΩ IT = 3.36 mAVS =38 V

=

Example Problem 5


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R1 =? Ω R2 =26 kΩ IT = 3.36 mA

Now we need to solve for I1

VS =38 V =

Example Problem 5


43


R1 =? Ω R2 =26 kΩ IT = 3.36 mA

Now we need to solve for I1 What equation has I1 in it?

VS =38 V =

Example Problem 5


44


R1 =? Ω R2 =26 kΩ IT = 3.36 mA

Now we need to solve for I1 What equation has I1 in it?

We have IT, can we solve for I2?

IT = I1 + I2 I1 = IT - I2or

VS =38 V =

Problem 5 Solution

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I2 = = =

Problem 5 Solution

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I2 = = = I2 = 0.00146 A = 1.46 mA

Problem 5 Solution

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I1 = IT – I2 = 3.36 mA – 1.46 mA Now that we have calculated the first value we

need, work back through the steps one by one

I2 = = = I2 = 0.00146 A = 1.46 mA

Problem 5 Solution

48




I2 = = = I2 = 0.00146 A = 1.46 mA

I1 = 1.9 mA

Problem 5 Solution

49




I2 = = = I2 = 0.00146 A = 1.46 mA

I1 = 1.9 mA =

Problem 5 Solution

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I2 = = = I2 = 0.00146 A = 1.46 mA

I1 = 1.9 mA =

Alternate Problem 5 Solution

Here is another formula to solve for R1

We can solve for RT with Ohm’s Law

Plug into above equation to solve for R1

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or

11309.5 -- 26000 ENTER ENTER

RT = = = 11309.5 Ω


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IT = I1 + I2 + I3 + I4 + …VS = VR1 = VR2 = VR3 = VR4 = …


For more than three resistors

+ + + …


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IT = I1 + I2 + I3 + I4 + …VS = VR1 = VR2 = VR3 = VR4 = …


For more than three resistors

Just keep adding terms for each new parallel path

+ + + …

What’s Next?

PracticePracticePractice

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Documents

1 Electronics Parallel Resistive Circuits Part 2 Copyright © Texas Education Agency, 2014. All rights reserved