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

More Complex Parallel Circuits Let’s do a parallel circuit analysis with three branches Follow the same analysis process as before 2 VSVS R1R1 R2R2 R3R3 Copyright © Texas Education Agency, All rights reserved.

More Complex Parallel Circuits 3 R1R1 R2R2 R3R3 I1I1 Copyright © Texas Education Agency, All rights reserved. VSVS

More Complex Parallel Circuits 4 R1R1 R2R2 R3R3 I2I2 Copyright © Texas Education Agency, All rights reserved. VSVS

More Complex Parallel Circuits 5 R1R1 R2R2 R3R3 I3I3 Copyright © Texas Education Agency, All rights reserved. VSVS

Parallel Circuit Equations 6 I T = I 1 + I 2 + I 3 V S = V R1 = V R2 = V R3 Copyright © Texas Education Agency, All rights reserved.

Parallel Circuit Equations 7 I T = I 1 + I 2 + I 3 V S = V R1 = V R2 = V R3 (current adds) (voltage is the same) (resistance is more complex, but it basically divides) Copyright © Texas Education Agency, All rights reserved. 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 8 S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, All rights reserved. VSVS

Understanding Resistance in a Parallel Circuit Close S 1 and L 1 comes on We get current I 1 from the battery Each light is identical Total current = I 1, total resistance = R 1 9 VSVS S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, All rights reserved.

Understanding Resistance in a Parallel Circuit Next close S 2 and S 3, L 2 and L 3 come on We get additional current I 2, I 3 from the battery Total current = I 1 + I 2 + I 3, triple the current This means total resistance must be cut to one third 10 S1S1 S2S2 S3S3 L1L1 L2L2 L3L3 Copyright © Texas Education Agency, All rights reserved. VSVS

Use the following formula: Assume R 1 = R 2 = R 3 = 30 Ω or Do the Math 11 Copyright © Texas Education Agency, All rights reserved.

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 12 Copyright © Texas Education Agency, All rights reserved.

Let’s try this first with two resistors Using the TI-83 buttons, perform the following Calculating Total Resistance ENTER Copyright © Texas Education Agency, All rights reserved.

Let’s try this first with two resistors Using the TI-83 buttons, perform the following If you did it right, 15 will be displayed You only enter resistance values and calculator functions Calculating Total Resistance ENTER Copyright © Texas Education Agency, All rights reserved.

Now try it for a circuit with three resistors Using the TI-83 buttons, perform the following Calculating Total Resistance ENTER Copyright © Texas Education Agency, All rights reserved.

Now try it for a circuit with three resistors Using the TI-83 buttons, perform the following If you did it right, 10 will be displayed Calculating Total Resistance ENTER Copyright © Texas Education Agency, All rights reserved.

Example Problem 1 For the following circuit, calculate R T and I T Begin by writing down the equations we need 17 Copyright © Texas Education Agency, All rights reserved. R 1 = 300 Ω R 2 = 200 Ω V S = 15 V and

Example Problem 1 18 Copyright © Texas Education Agency, All rights reserved ENTER 00

Example Problem 1 19 Copyright © Texas Education Agency, All rights reserved ENTER 00 R T = 120 Ω

Example Problem 1 20 Copyright © Texas Education Agency, All rights reserved ENTER 00 R T = 120 Ω

Example Problem 2 For the following circuit, calculate R T and I T Begin by writing down the equations we need We have enough information to solve these 21 Copyright © Texas Education Agency, All rights reserved. V S = 14.5 V R 1 = 1.4 kΩ R 2 = 2.2 kΩ R 3 = 1.8 kΩ and

Example Problem 2 22 Copyright © Texas Education Agency, All rights reserved.

Example Problem 2 23 Copyright © Texas Education Agency, All rights reserved. R T = 580 Ω

Example Problem 2 24 Copyright © Texas Education Agency, All rights reserved. R T = 580 Ω

Example Problem 2 25 Copyright © Texas Education Agency, All rights reserved. R T = 580 Ω I T = 25 mA

Example Problem 3 For the following circuit, calculate V S 26 Copyright © Texas Education Agency, All rights reserved. R 1 = 330 Ω R 2 = 560 Ω V S = ? I T = 106 mA

Example Problem 3 For the following circuit, calculate V S Write the equation that solves the problem 27 Copyright © Texas Education Agency, All rights reserved. R 1 = 330 Ω R 2 = 560 Ω V S = ? I T = 106 mA V S = V T = I T R T

Example Problem 3 For the following circuit, calculate V S Write the equation that solves the problem Look for what is needed to solve this equation We have I T, we need R T 28 Copyright © Texas Education Agency, All rights reserved. R 1 = 330 Ω R 2 = 560 Ω V S = ? I T = 106 mA V S = V T = I T R T

Example 3 Solution Write the equation for R T 29 Copyright © Texas Education Agency, All rights reserved.

Example 3 Solution Write the equation for R T 30 Copyright © Texas Education Agency, All rights reserved. R T = Ω

Example 3 Solution Write the equation for R T Plug this value into the first equation 31 Copyright © Texas Education Agency, All rights reserved. R T = Ω V S = V T = I T R T =.106 A Ω

Example 3 Solution Write the equation for R T Plug this value into the first equation 32 Copyright © Texas Education Agency, All rights reserved. R T = Ω V S = V T = I T R T =.106 A Ω V S = 22 V

Example Problem 4 Calculate R 1 33 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA V S = 20 V I T = 18 mA

Example Problem 4 Calculate R 1 Write the formula for R 1 34 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA I T = 18 mA V S = 20 V

Example Problem 4 Calculate R 1 Write the formula for R 1 Now we need a formula that solves for I 1 35 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA I T = 18 mA V S = 20 V

Example Problem 4 Calculate R 1 Write the formula for R 1 Now we need a formula that solves for I 1 36 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA I T = 18 mA I T = I 1 + I 2 V S = 20 V

Problem 4 Solution To calculate I 1, or 37 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA V S = 20 V I T = 18 mA I T = I 1 + I 2 I 1 = I T – I 2 I 1 = 18 mA – 10 mA = 8 mA

Problem 4 Solution To calculate I 1, or Plug into first formula 38 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA I T = 18 mA I T = I 1 + I 2 I 1 = I T – I 2 I 1 = 18 mA – 10 mA = 8 mA V S = 20 V

Problem 4 Solution To calculate I 1, or Plug into first formula 39 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω I 1 = ? R 2 = ? Ω I 2 = 10 mA V S = 20 V I T = 18 mA I T = I 1 + I 2 I 1 = I T – I 2 I 1 = 18 mA – 10 mA = 8 mA

Example Problem 5 For the following circuit calculate R 1 40 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω R 2 = 26 kΩ V S = 38 V I T = 3.36 mA

Example Problem 5 For the following circuit calculate R 1 Write the equation that solves the problem Note: there is more than one equation for R 1 Look for what is needed to solve this equation 41 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω R 2 = 26 kΩ I T = 3.36 mA V S = 38 V

Example Problem 5 For the following circuit calculate R 1 42 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω R 2 = 26 kΩ I T = 3.36 mA Now we need to solve for I 1 V S = 38 V

Example Problem 5 For the following circuit calculate R 1 43 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω R 2 = 26 kΩ I T = 3.36 mA Now we need to solve for I 1 What equation has I 1 in it? V S = 38 V

Example Problem 5 For the following circuit calculate R 1 44 Copyright © Texas Education Agency, All rights reserved. R 1 = ? Ω R 2 = 26 kΩ I T = 3.36 mA Now we need to solve for I 1 What equation has I 1 in it? We have I T, can we solve for I 2 ? I T = I 1 + I 2 I 1 = I T - I 2 or V S = 38 V

Problem 5 Solution 45 Copyright © Texas Education Agency, All rights reserved.

Problem 5 Solution 46 Copyright © Texas Education Agency, All rights reserved. I 2 = A = 1.46 mA

Problem 5 Solution 47 Copyright © Texas Education Agency, All rights reserved. I 1 = I T – I 2 = 3.36 mA – 1.46 mA Now that we have calculated the first value we need, work back through the steps one by one I 2 = A = 1.46 mA

Problem 5 Solution 48 Copyright © Texas Education Agency, All rights reserved. I 1 = I T – I 2 = 3.36 mA – 1.46 mA Now that we have calculated the first value we need, work back through the steps one by one I 2 = A = 1.46 mA I 1 = 1.9 mA

Problem 5 Solution 49 Copyright © Texas Education Agency, All rights reserved. I 1 = I T – I 2 = 3.36 mA – 1.46 mA Now that we have calculated the first value we need, work back through the steps one by one I 2 = A = 1.46 mA I 1 = 1.9 mA

Problem 5 Solution 50 Copyright © Texas Education Agency, All rights reserved. I 1 = I T – I 2 = 3.36 mA – 1.46 mA Now that we have calculated the first value we need, work back through the steps one by one I 2 = A = 1.46 mA I 1 = 1.9 mA

Alternate Problem 5 Solution Here is another formula to solve for R 1 We can solve for R T with Ohm’s Law Plug into above equation to solve for R 1 51 Copyright © Texas Education Agency, All rights reserved. or ENTER

Parallel Circuit Equations 52 I T = I 1 + I 2 + I 3 + I 4 + … V S = V R1 = V R2 = V R3 = V R4 = … Copyright © Texas Education Agency, All rights reserved. For more than three resistors

Parallel Circuit Equations 53 I T = I 1 + I 2 + I 3 + I 4 + … V S = V R1 = V R2 = V R3 = V R4 = … Copyright © Texas Education Agency, All rights reserved. For more than three resistors Just keep adding terms for each new parallel path

What’s Next? Practice 54 Copyright © Texas Education Agency, All rights reserved.