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Combined Series and Parallel Circuits

Combined Series and Parallel Circuits. Objectives: Calculate the equivalent resistance, current, and voltage of series and parallel circuits. Calculate the equivalent resistance of circuits combining series and parallel connections.

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Combined Series and Parallel Circuits

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  1. Combined Series and Parallel Circuits Objectives: Calculate the equivalent resistance, current, and voltage of series and parallel circuits. Calculate the equivalent resistance of circuits combining series and parallel connections. To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem. Solve circuit problems.

  2. Resistance and Current Series Circuit Equivalent resistance is equal to the sum of all the resistance in the circuit. Circuit current is equal to the voltage source divided by the equivalent resistance.

  3. Resistance and Current Parallel Circuit The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of the individual resistances. The total current is the sum of all the currents. The potential difference across each resistor is the same

  4. Household Circuits Small resistance from wiring Why do the lights dim when the hair dryer goes on? This is called a combination series and parallel circuit

  5. Series and Parallel Circuits • Draw a diagram of the circuit • Find any resistors in parallel. They must have the same potential difference across them. Calculate the single equivalent resistance of a resistor that can replace them. • Are any resistors (including the parallel equivalent resistor) in series? Resistors in series have one and only one current path through them. Calculate the new single equivalent resistance that can replace them. Draw a new schematic diagram using that resistor. • Repeat steps 2 and 3 until you can reduce the current to a single resistor. Find the total circuit current. Then go backwards to find the currents through and the voltages across individual resistors.

  6. Kirchhoff’s RulesGustav Kirchhoff - 1845 • The sum of the currents entering any junction must equal the sum of the currents leaving that junction. (junction rule) • The sum of the potential differences across all the elements around any closed circuit loop must equal zero. (loop rule)

  7. Now lets try some problems Don’t wait to get totally lost. Ask your questions as they come to you.

  8. #1 Series Circuit Rt = R1 + R2 + R3 + … Rt = 4 + 6 + 3 + 1 = 14  I = V  R I = 40  14 = 2.86 amps

  9. #2 Series Circuit Rt = R1 + R2 + R3 + … Rt = 5 + 4 + 12 = 21  I = V  R I = 10  21 = 0.476 amps

  10. #3 Series Circuit Rt = R1 + R2 + R3 + … Rt = 3 + 1 + 7 = 11  I = V  R I = 120  11 = 10.9 amps

  11. #4 Series Circuit Rt = R1 + R2 + R3 + … Rt = 5 + 1 + 6 + 3 + 4 + 1 = 20  I = V  R I = 9  20 = 0.45 amps

  12. #5 Series Circuit Rt = R1 + R2 + R3 + … Rt = 12 + 20 + 5 = 37  I = V  R I = 60  37 = 1.62 amps

  13. #6 Parallel Circuit 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt = 1/2 + 1/2 + 1/2 = 1.5 Rt = 0.667  I = V  R I = 6  0.667 = 9.00 amps

  14. #7 Parallel Circuit 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt = 1/6 + 1/8 + 1/4 = 0.542 Rt = 1.85  I = V  R I = 120  1.85 = 64.9 amps

  15. #8 Parallel Circuit 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt =1/2.5 + 1/6 + 1/1 = 1.57 Rt = 0.638  I = V  R I = 14  0.638 = 21.9 amps

  16. Now let’s put ‘em together Simplify diagram in steps to a single resistor Calculate total resistance and current for the whole circuit Then work backwards to find voltages and currents at individual resistors It takes time and care to do this right DON’T TRY TO RUSH THROUGH IT!

  17. #9 The 2  and 3  resistors are in series with one another They combine to form a 5  resistor

  18. The three resistors are hooked up in parallel with each other. 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt =1/5 + 1/1 + 1/6 = 1.37 Rt = 0.730  The circuit now looks like this I = V/R = 120/.730 = I = 164 amps

  19. #10 Combine the 3  and the 7  resistors that are in series with one another to make a 10  resistor Combine the 1  and the 2  resistor that are in series with one another to make a 3  resistor Then re-draw the circuit It should look like this

  20. The three resistors are hooked up in parallel with each other. 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt =1/10 + 1/4 + 1/3 = 0.683 Rt = 1.46  The circuit now looks like this I = V/R = 40/1.46 = I = 27.4 amps

  21. #11 Combine the resistors hooked up in series with one another and re-draw the circuit It should look like this

  22. The three resistors are hooked up in parallel with each other. 1/Rt = 1/R1 + 1/R2 + 1/R3 + … 1/Rt =1/4 + 1/4 + 1/10 = 0.600 Rt = 1.67  The circuit now looks like this I = V/R = 220/1.67 = I = 132 amps

  23. #12 What type of circuit is this? Find the total resistance Find the total current The ___________ is the same for all devices in a series circuit Therefore I3 = To find V2 we need to know… V = IR so V2 = 1.17(4) Series 12  1.17 amps Current 1.17 amps R2 and I2 4.68 V

  24. #13 What type of circuit is this? Find the total resistance Find the total current The ___________ is the same for all lines in a parallel circuit Therefore V3 = To find I3 we need to know… I = V/R so I3 = 120(2.5) Parallel 1.11  108 amps Voltage 120 V V3 & R3 48 amps

  25. #14 Both Is this a series or a parallel circuit? Combine the resistors in series first. Then re-draw the circuit. It should look something like this

  26. Now find the total resistance Do we need the total current? If so, what is it? How is resistor #5 hooked up? Those two resistors combine to form a resistor that is _____  How is that 5  resistor hooked up to the circuit? 2.4  No In series with #6 5  In parallel with the other combined resistors

  27. More about Resistor #5 What is the same for all the lines in a parallel circuit? What is the voltage across the 5  resistor? What is the current through that 5  resistor? What is the current through resistor #5? Why? V = IR V = 22(3) Voltage 110 V 22 amps 22 amps Series w/ #6 66 V

  28. Let’s look at Resistor #4 How is resistor #4 hooked up? Those two resistors combine to form a resistor that is __  How is that 11  resistor hooked up to the circuit? What is the same for all the lines in a parallel circuit? What is the voltage across the 11  resistor? In series with #3 11  Parallel with the other combined resistors Voltage 110 V

  29. More about Resistor #4 What is the current through that 11  resistor? What is the current through resistor #4? Why? 10 amps 10 amps Series w/ #3

  30. Now move on to the rest of the packet. We have the answers at all the problems. We have the solutions to #17 - #22. #23 is extra credit (it is really hard)

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