Physics 201. Professor P. Q. Hung. 311B, Physics Building. Physics 201 p. 1/3

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1 Physics 201 p. 1/3 Physics 201 Professor P. Q. Hung 311B, Physics Building

2 Physics 201 p. 2/3 Summary of last lecture Equipotential surfaces: Surfaces where the potential is the same everywhere, e.g. the surface of a conductor.

3 Physics 201 p. 2/3 Summary of last lecture Equipotential surfaces: Surfaces where the potential is the same everywhere, e.g. the surface of a conductor. Q = C V. C: Capacitance, the capacity to store charge

4 Physics 201 p. 2/3 Summary of last lecture Equipotential surfaces: Surfaces where the potential is the same everywhere, e.g. the surface of a conductor. Q = C V. C: Capacitance, the capacity to store charge U = 1 2 QV = 1 2 CV 2 = Q2 2C : potential energy of a capacitor

5 Physics 201 p. 3/3 Beyond electrostatic A current of 0.2 ma coming from a 3.0 V battery operates a calculator for one hour. How much charge flows in the circuit? In previous lectures, a conductor in electrostatic equilibrium: No electric field inside Conduction electrons do not flow.

6 Physics 201 p. 3/3 Beyond electrostatic A current of 0.2 ma coming from a 3.0 V battery operates a calculator for one hour. How much charge flows in the circuit? In previous lectures, a conductor in electrostatic equilibrium: No electric field inside Conduction electrons do not flow. For conduction electrons to start flowing together (current) in a given direction, we need an electric field.

7 Physics 201 p. 3/3 Beyond electrostatic A current of 0.2 ma coming from a 3.0 V battery operates a calculator for one hour. How much charge flows in the circuit? In previous lectures, a conductor in electrostatic equilibrium: No electric field inside Conduction electrons do not flow. For conduction electrons to start flowing together (current) in a given direction, we need an electric field. Difference in potential Electric field.

8 Physics 201 p. 4/3 Electric Current Difference in potential Electric field Conduction electrons move.

9 Physics 201 p. 4/3 Electric Current Difference in potential Electric field Conduction electrons move. How do we create such a potential difference? By connecting the two ends of the wire to the two terminals of a battery which posesses an electric potential difference.

10 Physics 201 p. 5/3 Electric Current How does a battery create a potential difference between its two terminals? By chemical reactions which transfer electrons from one terminal (making it positively charged) ( higher potential) to the other terminal (making it negatively charged) (lower potential).

11 Physics 201 p. 6/3 Electric Current

12 Physics 201 p. 7/3 Electric Current Is there a limit to the potential difference between the two terminals of a battery? Yes. It is called the electromotive force E (nothing to do with a force), e.g. E = 1.5 V for a AA battery.

13 Physics 201 p. 7/3 Electric Current Is there a limit to the potential difference between the two terminals of a battery? Yes. It is called the electromotive force E (nothing to do with a force), e.g. E = 1.5 V for a AA battery. How do the conduction electrons move? From low to high potential i.e. from - to +.

14 Physics 201 p. 7/3 Electric Current Is there a limit to the potential difference between the two terminals of a battery? Yes. It is called the electromotive force E (nothing to do with a force), e.g. E = 1.5 V for a AA battery. How do the conduction electrons move? From low to high potential i.e. from - to +. (Historical) convention: The direction of the current is taken to be from + to -, opposite to the direction of the electrons.

15 Physics 201 p. 8/3 Electric Current

16 Physics 201 p. 9/3 Electric Current How many electrons pass through a cross section of the wire in one second?

17 Physics 201 p. 9/3 Electric Current How many electrons pass through a cross section of the wire in one second? Current: I = q t

18 Physics 201 p. 9/3 Electric Current How many electrons pass through a cross section of the wire in one second? Current: I = q t Unit: 1 ampere(a) = 1 C/s

19 Physics 201 p. 10/3 Electric Current: Example A current of 0.2 ma coming from a 3.0 V battery operates a calculator for one hour. How much charge flows in the circuit? Answer: q = I t = ( A)(3600 s) = 0.72 C

20 Physics 201 p. 11/3 Electric current If the current is always in the same direction, you have a direct current or dc current; If the current oscillates, i.e. changes direction, you have an alternating or ac current.

21 Physics 201 p. 11/3 Electric current If the current is always in the same direction, you have a direct current or dc current; If the current oscillates, i.e. changes direction, you have an alternating or ac current. What is a typical speed of the electrons in a current? Answer: A rough calculation indicates that the average speed of the electrons called the drift speed is around m/s.

22 Physics 201 p. 12/3 Electric current So if I have a wire of length 2.4m, an electron at one end will take 10, 000 s to reach the other end. Why is it that when I flip the switch, the light immediately turns on? Answer: Just because the signal that turns on the electric field travels at the speed of light so that all electrons from one end to the other move at once.

23 Physics 201 p. 13/3 Ohm s Law How much current is flowing inside a circuit hooked to a battery? Take a ride on one of these electrons. You can actually see that it collides repeatedly with the atoms of the wire Resistance to the motion of that electron.

24 Physics 201 p. 14/3 Ohm s Law Any similarity with something that we already know? Yes. Imagine that you are sliding down a very icy slope. Because of negligible friction, most of the potential energy is converted into kinetic energy. If the slope is very rough instead, some of that potential energy is converted into heat.

25 Physics 201 p. 15/3 Ohm s Law The resistance is translated into a relationship between the applied voltage V and the current I: Ohm s Law: R = V I

26 Physics 201 p. 15/3 Ohm s Law The resistance is translated into a relationship between the applied voltage V and the current I: Ohm s Law: R = V I R: resistance. Unit: 1 ohm(ω) = 1 V A

27 Physics 201 p. 16/3 Ohm s Law: Example The resistance of a bagel toaster is 14 Ω. To prepare a bagel, the toaster is operated for one minute from a 120-V outlet. How much energy is delivered to the toaster? Three inputs: R = 14 Ω; t = 60 s; V = 120 V. Concepts?

28 Physics 201 p. 16/3 Ohm s Law: Example The resistance of a bagel toaster is 14 Ω. To prepare a bagel, the toaster is operated for one minute from a 120-V outlet. How much energy is delivered to the toaster? Three inputs: R = 14 Ω; t = 60 s; V = 120 V. Concepts? The energy delivered is equal to the work done in moving q in t = 60s and by a potential difference of 120 V. E = ( q) V.

29 Physics 201 p. 17/3 What s q? q = I t = V R t E = ( q) V = V 2 R J. Ohm s Law: Example t = (120V )2 14Ω (60s) =

30 Physics 201 p. 18/3 Resistance and Resistivity When I am given a piece of conducting wire, how do I know what its resistance might be? Answer: The electrons that travel from one end to the other encounter more atoms to scatter on as the wire gets longer. Also if the atoms are packed into a smaller area, there will be more scatterings The resistance will get larger.

31 Physics 201 p. 18/3 Resistance and Resistivity When I am given a piece of conducting wire, how do I know what its resistance might be? Answer: The electrons that travel from one end to the other encounter more atoms to scatter on as the wire gets longer. Also if the atoms are packed into a smaller area, there will be more scatterings The resistance will get larger. So?

32 Physics 201 p. 19/3 Resistance and Resistivity Empirical formula for the resistance: R = ρ L A ρ: Resistivity of the material L: Length of conducting wire A: Its cross-section

33 Physics 201 p. 19/3 Resistance and Resistivity Empirical formula for the resistance: R = ρ L A ρ: Resistivity of the material L: Length of conducting wire A: Its cross-section What does that tell us about different material? Conductors have low resistivity, while insulators have large resistivity. In general, we want to minimize the resistance.

34 Physics 201 p. 20/3 Resistance and Resistivity

35 Physics 201 p. 21/3 Resistance and Resistivity: Some aplications Impedance (or resistance) plethysmography: Measure the resistance in the calf, R = ρ L A = ρ L V calf /L = ρ L2 V calf. Pressure cuff cuts off the veinous flow V calf increases R decreases. Pressure cuff removed Rapid return to normal resistance if there is no blood clot in the veins. A slow return to normal indicates some blood clot.

36 Physics 201 p. 22/3 Resistance and Resistivity: Some aplications 20-gauge wire s cross section: m 2 ; 16-gauge wire s cross section: m 2. For the same length, the 16-gauge wire has smaller resistance than the 20-gauge one less heating (proportional to R) of the wire.

37 Physics 201 p. 23/3 Resistance and Resistivity: Some aplications If I heat up a wire, will its resistance change? Answer: The resistance goes up! For example, R = R 0 (1 + α(t T 0 )) where α is the temperature coefficient of resistivity.

38 Physics 201 p. 24/3 Resistance and Resistivity: Some aplications If I cool the wire to extremely low temperatures, what will happen to its resistance? Answer: There are some material whose resistance goes to zero as the temperature is lowered below some critical temperature T c. They are called superconductors. Copper oxide complexes such as Hg Ba 2 Ca 2 Cu 2 O 8+δ have T c = 150 K.

39 Physics 201 p. 25/3 Electrical energy and power From the example given above, the energy delivered to the toaster is U = qv = IV t

40 Physics 201 p. 25/3 Electrical energy and power From the example given above, the energy delivered to the toaster is The power is U = qv = IV t P = U t = IV = I 2 R = V 2 R

41 Physics 201 p. 26/3 Electrical energy and power For the toaster example above, P = 1.03kW

42 Physics 201 p. 26/3 Electrical energy and power For the toaster example above, P = 1.03kW From Eq. (5), one can see that, in order to minimize the power dissipated in terms of heat, one has to minimize the resistance.

43 Physics 201 p. 27/3 Resistors in series What happens to a circuit when I connect resistors in series, i.e. one after the other? Answer: In series means that the same current flows through the resistors.

44 Physics 201 p. 28/3 Resistors in series Let me take two resistors, R 1 and R 2. Can I simplify the problem? Answer: Yes. The voltages across the resistors are respectively V 1 = IR 1 and V 2 = IR 2. The sum is equal to the emf of the battery (neglecting internal resistance of the battery): V = V 1 + V 2 = IR 1 + IR 2 = I(R 1 + R 2 ) = IR eq. Equivalent resistance: R eq = R 1 + R

45 Physics 201 p. 29/3 Resistors in series So does that tell me that for a circuit with resistors in series, I can draw an equivalent circuit with one resistor whose resistance is the sum of all the individual resistances? Answer: Yes!

46 Physics 201 p. 30/3 Resistors in series

47 Physics 201 p. 31/3 Resistors in parallel How come all the wall sockets in my house have the same voltage, namely 120 V? Answer: This is an example of a wiring in parallel.

48 Physics 201 p. 31/3 Resistors in parallel How come all the wall sockets in my house have the same voltage, namely 120 V? Answer: This is an example of a wiring in parallel. What does it really mean? Answer: In parallel means that the devices (resistors, etc..) are connected in such a way that the voltage across each one of them is the same.

49 Physics 201 p. 32/3 Resistors in parallel What about the current(s)? Answer: Since I = V/R and V is the same, the one with larger R will have a smaller current flowing in it. There will be a current I i flowing in each branch i. The sum of all the currents in all the branches should be equal to the current produced by the source (battery,etc..) I = I 1 + I 2 + I

50 Physics 201 p. 33/3 Resistors in parallel Can I draw an equivalent circuit? Answer: Yes. I = I 1 + I 2 + I = V R 1 + V R = V R eq 1 R eq = 1 R R 2 +..

51 Physics 201 p. 34/3 Resistors in parallel

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