Chapter 22 Current and Resistance

Transcription

1 Chapter 22 Current and Resistance Chapter Goal: To learn how and why charge moves through a conductor as what we call a current. Slide 22-1

2 Chapter 22 Preview Looking Ahead Text: p. 702 Slide 22-2

3 Electric Current Electric current is a net flow of electric charge. Technically, the rate at which charge passes through a wire. I = dq/dt In a metal, the charge carriers are electrons. Although current is typically due to flowing electrons, we can pretend the current is due to flowing positive charges in opposite direction. Slide 22-3

4 Electric Current Outer valence electrons of metals are not really attached to any atom. They are free to randomly roam around. An electric field within the wire will cause these valence electrons to preferentially drift along wire in opposite direction of E field. Can pretend all valence electrons are flowing down wire with a drift velocity Stronger E fields produce higher drift velocities and thus higher current. Slide 22-4

5 QuickCheck 22.1 A wire carries a current. If both the wire diameter and the electron drift speed are doubled, the electron current increases by a factor of A. 2 B. 4 C. 6 D. 8 E. Some other value Slide 22-5

6 CT 29.2d A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. A B C Which region has the greatest magnitude electric field E? A, B, C, or D: All three are the same E: Not sure/not enough info?

7 EMF The Electromotive Force An electric field is needed to drive current through a wire. Where does the electric field in a current-carrying conductor come from? What keeps the current flowing over time? An emf device pumps charge from lower to higher potential energy, which maintains the charge separation that produces the E field throughout the circuit. Slide 22-7

8 Conceptual Example 22.4 Potential difference for batteries in a series Three batteries are connected one after the other as shown in FIGURE 22.15; we say they are connected in series. What s the total potential difference? Slide 22-8

9 Ohm s law Recall that the drift velocity is proportional to the electric field. The current is proportional to the drift velocity as well as the crosssectional area of the wire (as well as the density of valence electrons). Thus the current is proportional to E and A: Now the voltage difference across the wire of length L is Thus V = EL I / V L A Rearranging, V = I L A = IR I / EA ρ is resistivity (depends on material) R is resistance (depends on both material and geometry) Slide 22-9

10 Resistivity Slide 22-10

11 V = I L A = IR Slide 22-11

12 QuickCheck 22.7 The current through a wire is measured as the potential difference ΔV is varied. What is the wire s resistance? A Ω B Ω C. 50 Ω D. 100 Ω E. Some other value Slide 22-12

13 QuickCheck 22.8 Wire 2 is twice the length and twice the diameter of wire 1. What is the ratio R 2 /R 1 of their resistances? A. 1/4 B. 1/2 C. 1 D. 2 E. 4 Slide 22-13

14 Chapter 23 Preview Stop to Think Rank in order, from smallest to largest, the resistances R1 to R4 of the four resistors. Slide 22-14

15 Analyzing a Simple Circuit Consider a circuit using a battery, a lightbulb, and wires. The wires typically have a much lower resistance than that of the lightbulb. We ll pretend we have an ideal wire where its resistance is 0. The potential difference in the wire is 0, even if there is current in it. The voltage drop across the resistor is equal to the emf of the battery. Slide 22-15

16 Clicker Question A charge dq loses potential energy as it goes from one terminal of the battery to the other: U = dq E Where does the energy go? 1. Kinetic energy (drift velocity increases) 2. Thermal Energy 3. Internal potential energy Slide 22-16

17 Electric power and Ohmic Dissipation Emf source does positive work to bring charge back to positive terminal. If circuit has a current I, what is rate of work done by emf source? P bat = W t = q t E = EI P must be equal to rate of energy dissipation in resistor (Ohmic Dissipation): P Ohmic = VI = I 2 R Slide 22-17

18 Example Finding the current in a lightbulb How much current is drawn by a 75 W lightbulb connected to a 120 V outlet? Slide 22-18

19 Question Lightbulbs Two lightbulbs operate at 120 V, but one has a power rating of 25 W while the other has a power rating of 100 W. Which one has the greater resistance? 1) the 25 W bulb 2) the 100 W bulb 3) both have the same 4) this has nothing to do with resistance Slide 22-19

20 Example 22.5 Resistance of a lightbulb The glowing element in an incandescent lightbulb is the filament, a long, thin piece of tungsten wire that is heated by the electric current through it. When connected to the 120 V of an electric outlet, its power output is 60 W bulb. What is the current and the resistance of the filament? Slide 22-20

21 Clicker Question CT 29.6 US Bulbs are rated for 120 V. European bulbs are designed for 240 V. If you buy a 100 W light bulb as a souvenir in Paris, and plug it in at home, what happens? A: Glows as usual, like a 100 W bulb should B: Bzzzt, it burns out, too much power C: Glows half as bright (powerful) as usual D: It glows 1/4 as bright as usual E: None of these/???

22 Clicker Question