1. Combined Series and Parallel Circuits Objectives: 1. Calculate the equivalent resistance, current, and voltage of series and parallel circuits. 2. Calculate the equivalent resistance of circuits combining series and parallel connections. 3. To understand the origins of both of Kirchhoff's rules and how to use them to solve a circuit problem. 4. 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 Why do the lights dim when the hair dryer goes on? Small resistance from wiring This is called a combination series and parallel circuit

5. Series and Parallel Circuits 1.Draw a diagram of the circuit 2.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. 3.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. 4.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. 1.The sum of the currents entering any junction must equal the sum of the currents leaving that junction. (junction rule) 2.The sum of the potential differences across all the elements around any closed circuit loop must equal zero. (loop rule) Kirchhoff’s Rules Gustav Kirchhoff - 1845

7. Kirchhoff’s Rules Kirchhoff's first law when officially stated sounds more complicated than it actually is. Generally speaking, it says, the total current entering a junction must equal the total current leaving the junction. After all, no charges can simply disappear or get created, so current can't disappear or be created either. A junction is any place in a circuit where more than two paths come together. Kirchhoff's second law when officially stated sounds more complicated than it actually is. Generally speaking, it says, around any loop in a circuit, the voltage rises must equal the voltage drops. Another way of thinking about this is to consider that whatever energy a charge starts with in a circuit loop, it must end up losing all that energy by the time it gets to the end. Or we could say that by the time a charge makes it to the end of a circuit, it must have given all its energy to do work.

8. In this example you will notice that 8 Amps of current enter the junction and 3 and 5 Amps leave the junction. This makes a total of 8 Amps entering and 8 Amps leaving. In this example you will notice 8 Amps and 1 Amp entering the junction and 9 Amps leaving. This makes a total of 9 Amps entering and 9 Amps leaving. In this example you will notice 8 Amps and 1 Amp entering the junction while 7 Amps and 2 Amps leave. This makes a total of 9 Amps entering and 9 Amps leaving.

9. This is a simple circuit showing the potential differences across the source and the resistor. According to Kirchhoff's 2nd law the sum of the potential differences will be zero. This diagram shows the potentials in the little circles and then shows the potential differences off to the side. Notice that the potential difference is actually the difference between one potential and another. Moving from a low potential to a high potential is considered a potential rise or positive potential difference. Moving from a high potential to a lower potential is considered a potential drop or negative potential difference. This animation shows the same circuit as above but only looks at the potential differences as you go around the loop. Again, Kirchhoff's 2nd law says the sum of the potential differences has to be zero.

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

11. #1 Series Circuit R t = R 1 + R 2 + R 3 + … R t = 4 + 6 + 3 + 1 = 14  I = V  R I = 40  14 = 2.86 amps

12. #2 Series Circuit R t = R 1 + R 2 + R 3 + … R t = 5 + 4 + 12 = 21  I = V  R I = 10  21 = 0.476 amps

13. #3 Series Circuit R t = R 1 + R 2 + R 3 + … R t = 3 + 1 + 7 = 11  I = V  R I = 120  11 = 10.9 amps

14. #4 Series Circuit R t = R 1 + R 2 + R 3 + … R t = 5 + 1 + 6 + 3 + 4 + 1 = 20  I = V  R I = 9  20 = 0.45 amps

15. #5 Series Circuit R t = R 1 + R 2 + R 3 + … R t = 12 + 20 + 5 = 37  I = V  R I = 60  37 = 1.62 amps

16. #6 Parallel Circuit 1/R t = 1/R 1 + 1/R 2 + 1/R 3 + … 1/R t = 1/2 + 1/2 + 1/2 = 1.5 R t = 0.667  I = V  R I = 6  0.667 = 9.00 amps

17. #7 Parallel Circuit 1/R t = 1/R 1 + 1/R 2 + 1/R 3 + … 1/R t = 1/6 + 1/8 + 1/4 = 0.542 R t = 1.85  I = V  R I = 120  1.85 = 64.9 amps

18. #8 Parallel Circuit 1/R t = 1/R 1 + 1/R 2 + 1/R 3 + … 1/R t =1/2.5 + 1/6 + 1/1 = 1.57 R t = 0.638  I = V  R I = 14  0.638 = 21.9 amps