Bell Ringer: Define to the best of your ability the definition of: Current Voltage Resistance

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1 Bell Ringer: Define to the best of your ability the definition of: Current Voltage Resistance Explain the behavior of the current and the voltage in a Series Circuit. Explain the behavior of the current and the voltage in a Parallel Circuit.

2 Notes 7.4: Parallel Circuits This lesson promises to be ELECTRIFYING!

3 Learning on Your Own: All About Circuits All About Circuits Combination All About Circuits Analysis Technique All About Circuits Redrawing Combination Circuits

4 Lesson Objective: Recall the behavior of voltage, current, and resistance when objects are in series with one another. Recall the behavior of voltage, current, and resistance when objects are in parallel with one another. Determine how to solve for the voltage, current, resistance, and power when you have a combination circuit (series-parallel).

5 Combination Circuits: The world of circuitry is not strictly split into series circuits and parallel circuits. For instance, two objects may be in parallel with one another, but their total resistance may be in series with another resistor. Or two objects in series may have a total resistance that is in parallel with another resistor. Before we get started analyzing combination circuits, let s refresh on the behavior of voltage, current, and resistance in series and in parallel.

6 Series Circuits:

7 Series Circuits: Current is the same throughout. Anywhere current is measured, you will measure it to be the same as the total current in the circuit. Voltage change. Voltage is divided up between the different resistors but not equally. Series circuit is also called a voltage divider. V Battery = V 1 + V 2 + V 3 The total resistance between two or more resistors in series is given by: R eq = R 1 + R 2 + R 3

8 Parallel Circuits:

9 Parallel Circuits: Current changes. Current is split between the three resistors but not equally. Their total should add up to the total current before is divided by the two or more pathways. I T = I 1 + I 2 + I 3 Voltage stays the same. When two or more resistors are in parallel, they will always have the same voltage. The total resistance between two or more resistors in parallel is given by: R eq = 1 1 R1 + 1 R R 3

10 We can still use the table we have used before which I highly recommend. V=IR I=V/R R=V/I P=IV R 1 R 2 R 3 Total

11 Sample Problem 1

12 Sample Problem 1: Use the table method to determine the voltage, current, and resistance of each resistor.

13 Sample Problem 1: Use the table method to determine the voltage, current, and resistance of each resistor.

14 Sample Problem 1: Step 1: R 2 and R 3 are in parallel so combine the two resistors by using the equation R 2,3 = 1 1 R R3 = 3.3 Ω.

15 Sample Problem 1: R 2 and R 3 are in parallel so we can redraw this circuit as pictured below. Now we see the equivalent of R 2,3 is 3.3 Ω and it is in series with R 1.

16 Sample Problem 1: Since R 1 and R 2,3 are in series then we can simply add them to find the total resistance in the circuit. R T = R 1 + R 2,3 = 23.3 Ω.

17 Sample Problem 1: Since R 1 and R 2,3 are in series then we can simply add them to find the total resistance in the circuit. R T = R 1 + R 2,3 = 23.3 Ω.

18 Now, we have our table where know the total voltage is from the battery, and we have already calculated the total resistance. V=IR I=V/R R 1 R 2 R 3 Total 30 V R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

19 All we need are two objects to be able to calculate another quantity. Well we have our total voltage and total resistance so we can calculate our total current as: I = V R I = 1.3 A = 30 V 23.2 Ω V=IR I=V/R R=V/I P=IV Total 30 V 23.3 Ω

20 Now our chart looks like below. So what do we do next? R 1 R 2 R 3 Total V=IR 30 V I=V/R 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

21 Sample Problem 1: We trace the path of current. We know that the current is split between R 2 and R 3 but it is undivided as it goes through R 1. Therefore, I 1 is equivalent to the total current in the circuit.

22 Now our chart looks like below. Can we calculate anything else? R 1 R 2 R 3 Total V=IR 30 V I=V/R 1.3 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

23 We can calculate the voltage through resistor 1. V 1 = I 1 R 1 V 1 = (1.3 A)(20 Ω) V 1 = 26 V V=IR I=V/R R=V/I P=IV R A 20 Ω

24 Now our chart looks like below. Can we find V 2 and V 3? R 1 R 2 R 3 Total V=IR 26 V 30 V I=V/R 1.3 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

25 Since V 2 and V 3 are in parallel, we know their voltage will be the same. We also know that R 2,3 is in series with R 1. So what does that mean about the voltage? It means that V T = V 1 + V 2,3. V T = V 1 + V 2,3 30 V = 26 V + V 2,3 V 2,3 = 30 V 26 V V 2,3 = 4 V

26 Since V 2 and V 3 are in parallel than they are the same. R 1 R 2 R 3 Total V=IR 26 V 4 V 4 V 30 V I=V/R 1.3 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

27 Now we should be able to calculate I 2 and I 3 using I=V/R. R 1 R 2 R 3 Total V=IR 26 V 4 V 4 V 30 V I=V/R 1.3 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

28 I 2 + I 3 = 1.3 A which equals the total. R 1 R 2 R 3 Total V=IR 26 V 4 V 4 V 30 V I=V/R 1.3 A 0.4 A 0.9 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

29 Now we just have the power to find so let us use the equation P=IV. R 1 R 2 R 3 Total V=IR 26 V 4 V 4 V 30 V I=V/R 1.3 A 0.4 A 0.9 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV

30 Therefore our chart should be filled out as below: R 1 R 2 R 3 Total V=IR 26 V 4 V 4 V 30 V I=V/R 1.3 A 0.4 A 0.9 A 1.3 A R=V/I 20 Ω 10 Ω 5 Ω 23.3 Ω P=IV 33.8 W 1.6 W 3.6 W 39 W

31 Pay special attention to the total power. R 1 R 2 R 3 Total P=IV 33.8 W 1.6 W 3.6 W 39 W The reason why is because P T = P 1 + P 2 + P 3. Power is a great check to see if you did everything correctly. It DOES NOT MATTER if the circuit is in series, parallel, or any type of combination, the sum of the powers should add up to the total power. If P T = P 1 + P 2 + P 3 and P T = I T V T give the same result then you can be certain that you have done everything correctly.

32 Sample Problem 2

33 Sample Problem 2: Use the table method to determine the voltage, current, and resistance of each resistor.

34 Sample Problem 2: What do we notice about this circuit?

35 R 1 and R 2 are in series. We also see that that the total of R 1 and R 2 are in parallel with R 3.

36 Let s combine R 1 and R 2 by adding them together since they are in series. R 1,2 = R 1 + R 2 = 15Ω + 10 Ω = 25 Ω

37 Now we see that R 1,2 is in parallel with R 3. Now we have to find our total resistance.

38 R T = R T = 1 1 R 1,2 + 1 R3 1 1Τ 25 Ω + 1 Τ5 Ω R T = Ω R T = 4.17 Ω

39 Now let us fill out our table. R 1 R 2 R 3 Total V=IR 50 V I=V/R R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

40 Is there anything we can solve for now? R 1 R 2 R 3 Total V=IR 50 V I=V/R R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

41 Is there anything we can solve for now? I T = I T = V T RT 50 V 4.17 Ω I T = 12.0 A V=IR I=V/R R=V/I P=IV Total 50 V 4.17 Ω

42 Now our table looks like below. So what next? R 1 R 2 R 3 Total V=IR 50 V I=V/R 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

43 Well we know that the voltage across the resistor R 1,2 and R 3 will be the same as the battery voltage since they are in parallel with the battery (and the current does not go across another resistor before dividing between the two pathways). Therefore, V 1,2 = 50 V V 3 = 50 V

44 NOTE: Since the pathway of V 1,2 actually has two resistors which are in series on it than that means the voltage is split between the two resistors. In equation form: V 1 + V 2 = 50 V.

45 So, we don t actually know the voltage across R 1 or R 2 yet except that they add up to 50 V. V=IR I=V/R R 1 R 2 R 3 Total 50 V 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

46 However, we do know the voltage across R 3 is V 3 = 50 V. R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

47 This allows us to find I 3 = 50 VΤ 5 Ω = 10 A. R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

48 Does I 3 = 10 A make sense? R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

49 Absolutely because current wants to take the path of least resistance. R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

50 Are we able to determine the current going through the R 1,2 pathway? When objects are in parallel than we know that we can apply the equation: I T = I 1,2 + I 3 And in our case we have: 12 A = I 1, A I 1,2 = 12 A 10 A = 2 A

51 We also know that R 1 & R 2 are in series so what does that mean? They share the same current.

52 Since they share the same current, then that means: I 1 = 2 A I 2 = 2 A

53 So let us continue filling out our table. R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 2 A 2 A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

54 We are homeward bound, lets go find our voltage across R 1 & R 2 i.e. V 1 and V 2. R 1 R 2 R 3 Total V=IR 50 V 50 V I=V/R 2 A 2A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

55 V 1 = I 1 R 1 = 2 A 15 Ω = 30 V V 2 = I 2 R 2 = 2 A 10 Ω = 20 V R 1 R 2 R 3 Total V=IR 28.5 V 19 V 50 V 50 V I=V/R 2 A 2 A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

56 Does V 1 and V 2 add up to 50 V? If so then your answer is correct. R 1 R 2 R 3 Total V=IR 30 V 20 V 50 V 50 V I=V/R 2 A 2A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV

57 Let s find our powers now using P=IV. R 1 R 2 R 3 Total V=IR 30 V 20 V 50 V 50 V I=V/R 2 A 2A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV 60 W 40 W 500 W 600 W

58 Does P 1 + P 2 + P 3 = 600 W? R 1 R 2 R 3 Total V=IR 30 V 20 V 50 V 50 V I=V/R 2 A 2A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV 60 W 40 W 500 W 600 W

59 If so then that means you have done everything correctly. R 1 R 2 R 3 Total V=IR 30 V 20 V 50 V 50 V I=V/R 2 A 2A 10 A 12 A R=V/I 15 Ω 10 Ω 5 Ω 4.17 Ω P=IV 60 W 40 W 500 W 600 W

60 Exit Ticket

61 Complete the table to solve the circuit below.

62 Table will look like below. R 1 R 2 R 3 R 4 R 5 R 6 Total V=IR I=V/R R=V/I P=IV

63 EXAM EXTRA CREDIT

64 EXTRA CREDIT (15 Points): The current in resistance 6 is i 6 = 1.40 A and the resistances are R 1 = R 2 = R 3 = 2.00 Ω, R 4 = 16.0 Ω, R 5 = 8.00 Ω, and R 6 = 4.00 Ω. What is the emf of the ideal battery?

65 EXTRA CREDIT (15 Points): Determine current I 1 and I 2 in the circuit below:

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