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Chapter 25

Chapter 25. Current, Resistance, and Electromotive Force. Goals for Chapter 25. To understand current and how charges move in a conductor To understand resistivity and conductivity To calculate the resistance of a conductor To learn how an emf causes current in a circuit

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Chapter 25

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  1. Chapter 25 Current, Resistance, and Electromotive Force

  2. Goals for Chapter 25 • To understand current and how charges move in a conductor • To understand resistivity and conductivity • To calculate the resistance of a conductor • To learn how an emf causes current in a circuit • To calculate energy and power in circuits

  3. Current • Current is any motion of charge from one region to another. • Current I = dQ/dt[Amps] • E field in conductor causes charges to flow.

  4. Direction of current flow • A current can be produced by positive or negative charge flow. • Conventional current is treated as a flow of positive charges. • The moving charges in metals are electrons (see figure below).

  5. Current, drift velocity, and current density • Suppose: • n charged particles/volume • move w/ drift velocity vd • In time element dt • Cross-sectional area A • dQ = q (nAvd dt) • I = dQ/dt = nqAvd (scalar) • Define current density J • J = I/A = nqvd (vector)

  6. Current, drift velocity, and current density • Example: • 18 gauge wire (diameter = 1.02 mm); • current 1.67 A • 200 Watt lamp • Electron density = 8.5 x 1028/m3 . • What is J and vd?

  7. Resistivity • Resistivity of material = ratio of E field in material to current density it causes:  = E/J. • Large r implies a large E field is needed to generate small current!

  8. Resistivity • Conductivity is the reciprocal of the resistivity. • High conductivity means a large current results from a small applied E field.

  9. Resistivity and temperature • Resistivity depends on temperature. • ~ Linear R(T) = R0[1+a(T-T0)] • Table 25.2 shows some temperature coefficients of resistivity.

  10. Resistance • Resistance of a conductor is R = L/A [Ohms] • Potential decreases across a conductor is V = IR • Going from higher V to lower; in direction of current • V = IR (Ohm’s Law)

  11. Resistors are color-coded for easy identification • This resistor has a resistance of 5.7 kΩ with a tolerance of ±10%.

  12. Ohmic and nonohmic resistors • Only the resistor in Figure 25.10(a) below obeys Ohm’s law.

  13. Electromotive force and circuits • An electromotive force (emf) makes current flow. In spite of the name, an emf is not a force. • For simple complete circuits, EMF “pushes” current around from start to finish. • “EMF” is a voltage difference! • Ideal source – EMF is constant • Vab = E

  14. Electromotive force and circuits • Source of emf in an open circuit (left) • Source of EMG in complete circuit (right).

  15. Internal resistance • Real sources of emf actually contain some internal resistance r. • The terminal voltage of an emf source is Vab =  – Ir. • Terminal voltage of 12-V battery is less than 12 V when actually connected to the light bulb.

  16. Symbols for circuit diagrams • Table 25.4 shows the usual symbols used in circuit diagrams.

  17. Example 25.4 • EMF = 12 V; internal r = 2 Ohms. • What do ideal Voltmeter and Ammeter read?

  18. Source in a complete circuit • Now add a 4-Ohm resistor to the same source….

  19. Source in a complete circuit • Now add a 4-Ohm resistor to the same source…. V = IR = 2A x 4W = 8V V = 12V – 2A x 2W = 8V Ideal I = 12V/6 W = 2 A

  20. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits?

  21. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Ammeters measure flow of current PAST a point. Ideally, they should NOT influence the current Ideally, R(ammeter) = 0! Put them IN SERIES with circuit “legs”

  22. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeters measure pressure difference across (or between) points in the circuit. Ideally, they should NOT influence the current Ideally, R(voltmeter) = ! Put them in parallel!

  23. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits?

  24. Using voltmeters and ammeters What do Ammeters and Voltmeters do to circuits? Voltmeter in Series! R(voltmeter) =  No current will flow!

  25. A source with a short circuit • Without a resistor, what happens?

  26. Potential changes around a circuit • “Loop Rule”: • NET change in potential = zero for round trip in a circuit • EMF for loop equals sum of voltage “drops” across resistors or other elements.

  27. Energy and power in electric circuits • Rate energy is delivered to (or extracted from) a circuit element is P = VabI. • [POWER] = [WATTS] • Power delivered to pure resistor:P = I2R = Vab2/R.

  28. Energy and power in electric circuits • Rate energy is delivered to (or extracted from) a circuit element is P = VabI. • [POWER] = [WATTS] • Power delivered to pure resistor:P = I2R = Vab2/R.

  29. Power input and output • What are rates of energy conversion and power dissipation in circuit?

  30. Power input and output • What are rates of energy conversion and power dissipation in circuit? • Battery provides EI = 12 V x 2A = 24 Watts • Energy dissipation in battery = I2r = 8 Watts • Energy dissipation in 4W resistor = 16 Watts

  31. Power in a short circuit • Now power = 12 V x 6A = 72 W = I2R(internal)

  32. Theory of metallic conduction • Random motion of electrons in a conductor.

  33. PGE Rates & Meanings…. • PGE rates (10/3/12): • Small Businesses • $0.151/KWh (peak) • $0.136/KWh (off peak) • Home rates • $0.13/KWh (baseline to 351 kWh, winter) • $.034/KWh (max) • What’s a KWh??

  34. PGE Rates & Meanings…. • What’s a KWh?? • Kilowatt = 1000 Watts = 1000 Joules/Second • Kilowatt-hour = 1000 Watts x 3600 seconds • = 3.6 x 106 Joules = 3.6 MegaJoules • = 3.6 MJ • How much energy do I use? • 100W light bulb 5 hours at night to study physics? • 0.1 KW x 5 hours = 0.5 KWh @ $.13/KWh • Only 6.5 CENTS!!! (See!! Study physics!)

  35. PGE Rates & Meanings…. • What’s a KWh?? • Kilowatt = 1000 Watts = 1000 Joules/Second • Kilowatt-hour = 1000 Watts x 3600 seconds • = 3.6 x 106 Joules = 3.6 MegaJoules • = 3.6 MJ • How much energy do I use? • 100W light bulb 5 hours at night to study physics? • 0.1 KW x 5 hours = 0.5 KWh @ $.13/KWh • Only 6.5 CENTS!!! (See!! Study physics!)

  36. What do we use on average in the US? • ~ 960 KWh/residence/month2 (electricity) • ~ 12,000 KWh/year • ~ 80K – 90K KWh (80- 90 MWh) of energy from all sources per person per year1 • Sources: 1 US Department of Energy [Internet]. How much electricity does an American home use? 2012 Oct 3. http://www.eia.gov/tools/faqs/faq.cfm?id=97&t=3 • 2 Wikipedia contributors. Energy in the United States [Internet]. Wikipedia, The Free Encyclopedia; 2012 Oct 12:48 UTC [cited 2012 Oct 3]. Available from: http://en.wikipedia.org/w/index.php?title=Energy_in_the_United_States&oldid=515617945.2

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