1. Chapter 18 EMF Parallel Circuits Series Circuits

3. So, when the electric company sends you a bill at the end of the month, what are they charging you for? Well, what are the units of the quantity for which they bill you? Kilowatt-Hours 10 3 W - Hours 10 3 (J/s) Hours 10 3 (J/s) Hours (3600 s/Hour) 3.6 X 10 6 J

4. We’ve looked at simple series and parallel circuits involving batteries and capacitors. We now examine series and parallel circuits involving batteries and resistors. We’ll confine our comments in this chapter to “direct current” circuits – that is, circuits in which the current flows in only one direction. DC Circuits

5. The “electromotive force” The term “electromotive force” has fallen out of favor since it really is not a force at all! However, the term “EMF” has stuck and is used in the description of devices which increase the potential energy of charges flowing in a circuit. Such devices are called sources of emf.

6. You’ve probably noticed by now that we physicists use the letter “E” an awful lot… There’s energy and electric fields, besides the e representing the exponential function... Well, guess what letter is used to represent the new quantity “emf?”

7. So, in an attempt to minimize your confusion over the different E’s, I will use the following notation... E represents Energy E represents the Electric Field And  represents the EMF. Watch out! This is slightly different than the book!

8. + _ For the case of a battery with no internal resistance  = V The EMF and the potential are closely related. In fact, they have the same units: Volts.

9. Of course, real batteries have some internal resistance, such that V R  R int I V =  - I R int load resistor internal resistance terminal voltage

10. V R  R int I What is the current in this circuit?  = I R int + I R  I = R int + R What is the power supplied by the EMF? What is the power supplied by the battery? P = I V = I 2 R So what happened to the difference? P = I  = I 2 (R int + R)

11. The lost power in the battery (or resistor) that goes into heating it. Check out the temperature of rechargeable batteries next time you use them... “Joule Heating”

12. For MOST cases we will deal with R int << R so we usually neglect R int Unless otherwise stated R int = 0!

13. But many other devices are designed to take advantage of Joule heating. Perhaps you can think of a few? Joule heating in a battery is not desirable -- it’s power lost in the battery that cannot be used by the other devices in the circuit.

14. So, what happens after the battery is connected to this circuit? V 1 + V 2 = V I 1 = I 2 due to conservation of charge! V R2R2 + _ R1R1 I1I1 I2I2

15. We can construct an equivalent circuit with a single resistor... V = V 1 + V 2 = I R 1 + I R 2 = I ( R 1 + R 2 ) V R2R2 + _ R1R1 I I V = I R eq V R eq + _ I

16. R eq = R 1 + R 2 Resistors in series ADD. V R eq + _ V = V 1 + V 2 = I R 1 + I R 2 = I ( R 1 + R 2 ) V = I R eq

17. What happens in a series circuit if one of the resistors burns out? V R2R2 + _ R1R1 I I = 0 When one element fails, the circuit is broken; the current ceases to flow; and all the other elements (in the same branch of the circuit) stop functioning as well.

18. Old Christmas tree lights used to be wired in series. When one bulb burned out, the whole string of lights went dark. Figuring out which bulb had failed could be quite a chore!

19. Is there any time you might want to use a series circuit? Well, a fuse box or circuit breaker box is a good place to use a series circuit. When the appliances in your house draw too much current, a potential fire hazard exists. (Too much current leads to too much joule heating of the wires.) Circuit breakers and fuses are designed to fail when the currents through them become too large.

20. By sending power into your house through a circuit breaker or fuse, you prevent large currents from entering the house. The circuit breaker (fuse) is wired in series with the electrical outlets in the house. The outlets are actually wired in parallel with each other. Breaker Box Outlets with Appliances I

21. When the breaker is tripped, current ceases to flow to the outlets connected to that circuit in the house. Breaker Box Outlets with Appliances No Current!

23. So, what happens after the battery is connected to this circuit? The current divides, with part of it going through R 1 and part of it going through R 2. V R2R2 + _ R1R1 The voltage across R 1 and R 2 must be the same! I I1I1 I2I2 Just like capacitors in parallel!