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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

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