1. Chapter 26 DC Circuits

2. I The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value. 25-6 Power in Household Circuits

3. I Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced. 25-6 Power in Household Circuits

4. I Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset. 25-6 Power in Household Circuits

5. I Example 25-11: Will a fuse blow? Determine the total current drawn by all the devices in the circuit shown.

6. I 25-6 Power in Household Circuits Conceptual Example 25-12: A dangerous extension cord. Your 1800-W portable electric heater is too far from your desk to warm your feet. Its cord is too short, so you plug it into an extension cord rated at 11 A. Why is this dangerous?

7. I Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC). 25-7 Alternating Current

8. I The voltage varies sinusoidally with time: as does the current: 25-7 Alternating Current, f is the frequency, and is 60Hz in the US and Canada, and 50Hz in Europe I 0 is the peak current

9. I Multiplying the current and the voltage gives the power: 25-7 Alternating Current This the average power

10. I Usually we are interested in the average power: 25-7 Alternating Current

11. I The current and voltage both have average values of zero, so we square them, take the average, then take the square root, yielding the root-mean-square (rms) value: 25-7 Alternating Current

12. I Problem 54 54.(II) (a) What is the maximum instantaneous power dissipated by a 2.5-hp pump connected to a 240- Vrms ac power source? (b) What is the maximum current passing through the pump?

13. I Electrons in a conductor have large, random speeds just due to their temperature. When a potential difference is applied, the electrons also acquire an average drift velocity, which is generally considerably smaller than the thermal velocity. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity

14. I We define the current density (current per unit area) – this is a convenient concept for relating the microscopic motions of electrons to the macroscopic current: If the current density is not uniform:.

15. I This drift speed v d is related to the current in the wire, and also to the number of electrons per unit volume: 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity V is the volume and

16. I 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity The electric field inside a current-carrying wire can be found from the relationship between the current, voltage, and resistance. Writing R = ρ l /A, I = jA, and V =E l, and substituting in Ohm’s law gives:  Is the resistivity and σ is the conductivity =1/ 

17. I Electric circuit needs battery or generator to produce current – these are called sources of electromotive force (emf). emf is not a force but a voltage Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf. 26-1 EMF and Terminal Voltage

18. I This resistance behaves as though it were in series with the emf. 26-1 EMF and Terminal Voltage

19. I Electric Current and the Human Body < 5 mA- No harm 10 – 20 mA – Involuntary muscle contraction or paralysis, burns 100 – 300 mA – Ventricular fibrillation Shock disturbs heart rhythm Shock restores heart rhythm

20. I Resistance and the Human body I=V/R Most resistance is due to skin Dry resistance-- 10k  1M  Wet or sweaty-- 1000  1.00 If V= 120 V R I (mA) 1M  10k  1k  0.12 12 120

21. I Problem 3 3.(II) A 1.5-V dry cell can be tested by connecting it to a low-resistance ammeter. It should be able to supply at least 25 A. What is the internal resistance of the cell in this case, assuming it is much greater than that of the ammeter?

22. I 26-1 EMF and Terminal Voltage Example 26-1: Battery with internal resistance. A 65.0-Ω resistor is connected to the terminals of a battery whose emf is 12.0 V and whose internal resistance is 0.5 Ω. Calculate (a) the current in the circuit, (b) the terminal voltage of the battery, V ab, and (c) the power dissipated in the resistor R and in the battery’s internal resistance r.

23. I A series connection has a single path from the battery, through each circuit element in turn, then back to the battery. 26-2 Resistors in Series and in Parallel

24. I The current through each resistor is the same; the voltage depends on the resistance. The sum of the voltage drops across the resistors equals the battery voltage: 26-2 Resistors in Series and in Parallel

25. I From this we get the equivalent resistance (that single resistance that gives the same current in the circuit): 26-2 Resistors in Series and in Parallel

26. I A parallel connection splits the current; the voltage across each resistor is the same: 26-2 Resistors in Series and in Parallel

27. I The total current is the sum of the currents across each resistor: 26-2 Resistors in Series and in Parallel,

28. I This gives the reciprocal of the equivalent resistance: 26-2 Resistors in Series and in Parallel

29. I Problem 8 8. (I) How many 10V resistors must be connected in series to give an equivalent resistance to five 100V resistors connected in parallel?

30. I An analogy using water may be helpful in visualizing parallel circuits. The water (current) splits into two streams; each falls the same height, and the total current is the sum of the two currents. With two pipes open, the resistance to water flow is half what it is with one pipe open. 26-2 Resistors in Series and in Parallel

31. I Circuit Analysis Principles Need to find I through each element current (charge) splits at junctions Current (charge) is the same in series V across each element or set Voltages add in series Voltages are same in parallel Voltages around a loop sum to zero