1 electronics parallel resistive circuits part 2 copyright © texas education agency, 2014. all...

Electronics

ParallelResistive

CircuitsPart 2

More Complex Parallel Circuits

Let’s do a parallel circuit analysis with three branches

Follow the same analysis process as before

VS R1 R2 R3

R1 R2 R3I1

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

VS = VR1 , so from Ohm’s Law

R1 R2 R3I2

R1 R2 R3I3

Parallel Circuit Equations

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

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

S1 S2 S3

L1 L2 L3

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

S1 S2 S3

L1 L2 L3

Use the following formula:

Assume R1 = R2 = R3 = 30 Ω

Do the Math

+ + + +

.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

Let’s try this first with two resistors

Using the TI-83 buttons, perform the following

Calculating Total Resistance

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

3 0 + 3 0 ENTER ENTER

Now try it for a circuit with three resistors

3 0 + 3 0

3 0 ENTER

Now try it for a circuit with three resistors

If you did it right, 10 will be displayed

3 0 + 3 0

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

3 0 + 2 0

ENTER ENTER

Example Problem 1

3 0 + 2 0

ENTER ENTER

RT = 120 Ω

Example Problem 1

3 0 + 2 0

ENTER ENTER

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

RT = 580 Ω + + +

Example Problem 2

RT = 580 Ω + + +

IT = = =

Example Problem 2

RT = 580 Ω + + +

IT = = = 0.025 AIT = 25 mA

Example Problem 3

For the following circuit, calculate VS

R1 =330 Ω R2 =560 Ω VS = ?IT = 106 mA

Example Problem 3

Write the equation that solves the problem

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

R1 =330 Ω R2 =560 Ω VS = ?IT = 106 mA

VS = VT = IT • RT

Example 3 Solution

Write the equation for RT

Example 3 Solution

RT = 207.6 Ω =

Example 3 Solution

Plug this value into the first equation

RT = 207.6 Ω =

VS = VT = IT • RT = .106 A • 207.6 Ω

Example 3 Solution

Plug this value into the first equation

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

Example Problem 4

Calculate R1

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

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

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

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

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

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

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

Example Problem 5

R1 =? Ω R2 =26 kΩ IT = 3.36 mA

Now we need to solve for I1

VS =38 V =

Example Problem 5

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

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

I2 = = =

Problem 5 Solution