# College Physics B - PHY2054C

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1 Power College - PHY2054C and 09/15/2014 My Office Hours: Tuesday 10:00 AM - Noon 206 Keen Building

2 PHY2054C Power First Mini-Exam this week on Wednesday!! Location: UPL 101, 10:10-11:00 AM Exam on chapters 19, 20 & 21 forces & fields; Coulomb s Law & Gauss s Law potential & electric potential energy current, resistors & capacitors Equation sheet will be provided. Do not forget to bring your student ID!

3 Power Review: Potential The electric potential V is proportional to the electric potential energy. If the electric potential energy of a charge q at a particular location is PE elec, the electric potential at that point is V = PE elec q.

4 Power Review: potential The electric potential V is proportional to the electric potential energy. Suppose the potential changes by an amount V over a distance x. The component of the electric field along this direction is then E = V x.

5 Power Capacitance Potential of a capacitor: E = Q ǫ 0 A = V d V = Q d ǫ 0 A = E d Capacitance C is defined as: V = Q C C = ǫ 0 A d Parallel-Plate Capacitor

6 Power Review Question 1 phet.colorado.edu/en/simulation/capacitor-lab Four 16 µf capacitors are connected in series. The equivalent capacitance of this combination is A 64.0 µf B 16.0 µf C 4.0 µf D 2.0 µf

7 Power Review Question 1 phet.colorado.edu/en/simulation/capacitor-lab Four 16 µf capacitors are connected in series. The equivalent capacitance of this combination is A 64.0 µf B 16.0 µf C 4.0 µf D 2.0 µf When two capacitors are connected in series, they act as a single equivalent capacitance with a value 1 C equiv = 1 C C 2 and Q = Q 1 = Q 2

8 Power Review Question 2 phet.colorado.edu/en/simulation/capacitor-lab Four 16 µf capacitors are now connected in parallel. The equivalent capacitance of this combination is A 64.0 µf B 16.0 µf C 4.0 µf D 2.0 µf

9 Power Review Question 2 phet.colorado.edu/en/simulation/capacitor-lab Four 16 µf capacitors are now connected in parallel. The equivalent capacitance of this combination is A 64.0 µf B 16.0 µf C 4.0 µf D 2.0 µf When two capacitors are connected in parallel, they act as a single equivalent capacitance with a value C equiv = C 1 + C 2 and Q = Q 1 + Q 2

10 Outline Power 1 2 Power 3

11 Power The motion of charges leads to the idea of electric circuits: current, I, in a wire is defined as the net amount of charge that passes through it per unit time at any point: Current I = Q t The unit of electric current: [ ] C = [ A ] Ampere s Current is defined in terms of net positive charge flow.

12 Current Power André-Marie Ampère (22 January June 1836) current is the flow of electric charge (a phenomenon) or the rate of flow of electric charge (a quantity). This flowing electric charge is typically carried by moving electrons, in a conductor such as wire; in an electrolyte, it is instead carried by ions, and, in a plasma, by both.

13 Direction of the Current Power current flow device + - [battery symbol]

14 Direction of the Current Power 1 If the current is carried by positive charges moving with a given velocity, the direction of the current is parallel to the velocity. 2 If the current is carried by negative charges, the direction of the current is opposite the charges velocity.

15 Power Current and Potential Energy For charge to move along a wire, the electric potential energy at one end of the wire must be higher than the electric potential energy at the other end. potential is related to electric potential energy: V = PE elec / q The potential is referred to simply as voltage. The direction of I is always from high to low potential, regardless if the current is carried by + or charges.

16 Simple Circuit Power If the battery terminals are connected to two ends of a wire, a current is produced: Electrons move out of the negative terminal of the battery through the wire and into the positive battery terminal. The chemical reaction moves charge internally between the electrodes. No net charge accumulates on the battery terminals while the current is present. Battery will run down.

17 Outline Power 1 2 Power 3

18 Power 1 Drag force on electrons leads to a drift velocity proportional to the force pushing the electrons. 2 Force is proportional to the electric field, so the drift velocity is proportional to the field. 3 The electric field is proportional to the potential difference, so the drift velocity is proportional to the potential difference. 4 The current is proportional to the drift velocity, so the current is proportional to the potential difference: V ohmic device slope = R I = V R Unit of R : Ohm s Law [ ] V A = [Ω] I

19 Power George Simon Ohm (16 March July 1854) Ohm s law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them. :

20 Resistivity Power The resistivity, ρ, depends only on the material used to make the wire. of a wire of length L and cross sectional area A is given by: Material ρ [Ω m ] R = ρ L A Copper Glass 1 to Silicon 0.1 to 100

21 Power Resistors All electronic devices, from heaters to light bulbs to stereo amplifiers, offer resistance to the flow of current and are therefore considered resistors. Resistors can be made in many shapes and sizes. Each will have a resistance proportional to the current through and the potential across the resistor. Many, but not all, materials and devices obey. is not a fundamental law of nature. Resistors do obey.

22 Power The circuit diagram (A) shows the symbols for the resistor and the battery. Since the resistance of the wires is much smaller than that of the resistors, a good approximation is R wire = 0. If the circuit is open, there is no current flow anywhere in the circuit. Circuit Schematic

23 Circuit Symbols Power

24 Power Energy in a Resistor Power The test charge gained energy when it passed through the battery. It lost energy as it passed through the resistor. Energy is converted into heat energy inside the resistor: The energy is dissipated as heat. It shows up as a temperature increase of the resistor and its surroundings. P (Power) = energy transformed time = Q V t = I V P = I V = I 2 R = V 2 / R Reminder: : R = V / I Power

25 Power of a Light Bulb What is a typical household light bulb? 60 Watt light bulb What is a typical household voltage? 110 Volts What else do we know? P = V I = V 2 / R R = V 2 P = (110 V)2 60 W 200 Ω Battery-Resistor Circuit: phet.colorado.edu/en/simulation/battery-resistor-circuit

26 Power Question 3 In the US and Canada, the standard line voltage is VRMS = 110 V. In much of the world (Europe, Australia, Asia), the standard line voltage is VRMS = 220 V. The light output of a 60 Watt Tallahassee light bulb if used in Europe would A be twice as bright. Hint: Think about B be four times as bright. C be half as bright. P = V I = V 2 / R D be one fourth as bright. E remain the same brightness.

27 Power Question 3 In the US and Canada, the standard line voltage is VRMS = 110 V. In much of the world (Europe, Australia, Asia), the standard line voltage is VRMS = 220 V. The light output of a 60 Watt Tallahassee light bulb if used in Europe would A be twice as bright. B be four times as bright. P = V I = V 2 / R C be half as bright. It must get brighter. D be one fourth as bright. E remain the same brightness.

28 Power Question 3 In the US and Canada, the standard line voltage is VRMS = 110 V. In much of the world (Europe, Australia, Asia), the standard line voltage is VRMS = 220 V. The light output of a 60 Watt Tallahassee light bulb if used in Europe would B be four times as bright. P = V I = V 2 / R How much brighter? P Europe V 2 Europe = 1 R = P USA V 2 USA P Europa = P USA V 2 Europe V 2 USA P Europa = 4 P USA

29 Power P lost = I 2 R and P = V I P lost = ( PD V D ) 2 R High Voltage is Better.

30 Power lightbulbs are rated in watts. Incandescent Lamps Incandescent lamps are relatively inefficient as light sources. Typically, less than 5 % of the electrical energy is converted to visible light. Most of the energy produced is invisible infrared radiation and heat (resistive heating).

31 Power lightbulbs are rated in watts. Incandescent Lamps Incandescent lamps are relatively inefficient as light sources. Typically, less than 5 % of the electrical energy is converted to visible light. Most of the energy produced is invisible infrared radiation and heat (resistive heating). New technologies have greatly reduced the watts, saving the lumens: Halogen, compact fluorescent, LED.

32 Power lightbulbs are rated in watts. Incandescent Lamps Incandescent lamps are relatively inefficient as light sources. Typically, less than 5 % of the electrical energy is converted to visible light. Most of the energy produced is invisible infrared radiation and heat (resistive heating). New technologies have greatly reduced the watts, saving the lumens: Halogen, compact fluorescent, LED.

33 Resistivity & Temperature Power of a metal wire: R = ρ L A In general, the resistance of metal increases with temperature: ρ T = ρ 0 [ 1 + α (T T 0 )] Temperature Coefficients Material α [(C ) 1 ] Silver Copper Silicon 0.07

34 Outline Power 1 2 Power 3

35 Power When current passes through one resistor and then another, the resistors are said to be in series: E I R 1 I R 2 = 0 Kirchhoff s Loop Rule Any number of resistors can be connected in series. The resistors will be equivalent to a single resistor with: R equiv = R 1 + R 2 + R

36 Power In some circuits, the current can take multiple paths: The different paths are called branches. The arrangement of resistors shown is called resistors in parallel. Amount of current entering a junction must be equal to the current leaving it.

37 Power Applying the Junction Rule (Kirchhoff s Junction Rule) For path 1, +E I 1 R 1 = 0 For path 2, +E I 2 R 2 = 0 The total current is: I 3 = I 1 + I 2 = E R 1 + E R 2 = E ( 1 R R 2 )

38 Equivalent - Parallel Power

39 Circuit Analysis Power 1 Some complex circuits can be solved by combinations of series and parallel rules. 2 Other circuits must be analyzed directly by Kirchhoff s Rules. Loop Rule: The total change in the electric potential around any closed circuit path must be zero. Junction Rule: The current entering a circuit junction must equal the current leaving the junction. 3 Connecting resistors in series always gives a total resistance larger than the resistance of any of the component resistors. 4 Connecting resistors in parallel always gives a total resistance smaller than the resistance of any of the component resistors.

40 Ammeters Power An Ammeter is a device that measures current. An ammeter must be connected in series with the desired circuit branch. An ideal ammeter will measure current without changing its value. Must have a very low resistance.

41 Voltmeters Power A Voltmeter is a device that measures the voltage across a circuit element. It must be connected in parallel with the element. An ideal voltmeter should measure the voltage without changing its value. Should have a very high resistance.

42 and Nerves Power Many nerves are long and thin, much like wires. The conducting solution inside the fiber acts as a resistor. The lipid layer acts as a capacitor. The nerve fiber behaves as an RC circuit. More on RC circuits next week! Your body is a moderately good conductor of electricity. The body s resistance when dry is about 1500 Ω. When wet, the body s resistance is about 500 Ω. Current is carried by different parts of the body: Skin, internal organs,...

43 Power At very low temperatures, the linearity of resistance breaks down. The resistivities of metals approach a nonzero value at very low temperatures. In some metals, resistivity drops abruptly and is zero below a critical temperature. These metals for which the resistivity goes to zero are the called superconductors.

44 Power John Robert Schrieffer Nobel Laureate Emeritus Professor at Florida State Bardeen, Cooper, and Schrieffer received the Nobel Prize in 1972 for the development of the theory of superconductivity. The BCS Theory is one of the greatest discoveries of the 20th century.

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