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Understanding Electric Currents and Resistance: A Comprehensive Overview

Explore the concepts of electric currents, resistance, AC and DC currents, microscopic views, superconductivity, and DC circuits in this detailed chapter. Learn about drift velocity, current density, power calculations, and more.

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Understanding Electric Currents and Resistance: A Comprehensive Overview

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  1. Chapter 25Electric Currents and Resistance

  2. 25-7 Alternating Current Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC).

  3. 25-7 Alternating Current , The voltage varies sinusoidally with time: , as does the current:

  4. 25-7 Alternating Current Multiplying the current and the voltage gives the power:

  5. 25-7 Alternating Current . Usually we are interested in the average power:

  6. 25-7 Alternating Current 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:

  7. 25-7 Alternating Current Example 25-13: Hair dryer. (a) Calculate the resistance and the peak current in a 1000-W hair dryer connected to a 120-V line. (b) What happens if it is connected to a 240-V line in Britain?

  8. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity 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.

  9. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity . 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 is not uniform:

  10. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity This drift speed is related to the current in the wire, and also to the number of electrons per unit volume: and

  11. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity Example 25-14: Electron speeds in a wire. A copper wire 3.2 mm in diameter carries a 5.0-A current. Determine (a) the current density in the wire, and (b) the drift velocity of the free electrons. (c) Estimate the rms speed of electrons assuming they behave like an ideal gas at 20°C. Assume that one electron per Cu atom is free to move (the others remain bound to the atom).

  12. 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, andV = El , and substituting in Ohm’s law gives:

  13. 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity Example 25-15: Electric field inside a wire. What is the electric field inside the wire of Example 25–14? (The current density was found to be 6.2 x 105 A/m2.)

  14. 25-9 Superconductivity In general, resistivity decreases as temperature decreases. Some materials, however, have resistivity that falls abruptly to zero at a very low temperature, called the critical temperature, TC.

  15. 25-9 Superconductivity Experiments have shown that currents, once started, can flow through these materials for years without decreasing even without a potential difference. Critical temperatures are low; for many years no material was found to be superconducting above 23 K. Since 1987, new materials have been found that are superconducting below 90 K, and work on higher temperature superconductors is continuing.

  16. Summary of Chapter 25 • A battery is a source of constant potential difference. • Electric current is the rate of flow of electric charge. • Conventional current is in the direction that positive charge would flow. • Resistance is the ratio of voltage to current:

  17. Summary of Chapter 25 • Ohmic materials have constant resistance, independent of voltage. • Resistance is determined by shape and material: • ρ is the resistivity.

  18. Summary of Chapter 25 • Power in an electric circuit: • Direct current is constant. • Alternating current varies sinusoidally:

  19. Summary of Chapter 25 • The average (rms) current and voltage: • Relation between drift speed and current:

  20. Chapter 26DC Circuits

  21. Units of Chapter 26 • EMF and Terminal Voltage • Resistors in Series and in Parallel • Kirchhoff’s Rules • Series and Parallel EMFs; Battery Charging • Circuits Containing Resistor and Capacitor (RC Circuits) • Electric Hazards • Ammeters and Voltmeters

  22. 26-1 EMF and Terminal Voltage Electric circuit needs battery or generator to produce current – these are called sources of emf. Battery is a nearly constant voltage source, but does have a small internal resistance, which reduces the actual voltage from the ideal emf:

  23. 26-1 EMF and Terminal Voltage This resistance behaves as though it were in series with the emf.

  24. 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, Vab, and (c) the power dissipated in the resistor R and in the battery’s internal resistance r.

  25. 26-2 Resistors in Series and in Parallel A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.

  26. 26-2 Resistors in Series and in Parallel 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:

  27. 26-2 Resistors in Series and in Parallel From this we get the equivalent resistance (that single resistance that gives the same current in the circuit):

  28. 26-2 Resistors in Series and in Parallel A parallel connection splits the current; the voltage across each resistor is the same:

  29. 26-2 Resistors in Series and in Parallel The total current is the sum of the currents across each resistor: ,

  30. 26-2 Resistors in Series and in Parallel This gives the reciprocal of the equivalent resistance:

  31. 26-2 Resistors in Series and in Parallel 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.

  32. 26-2 Resistors in Series and in Parallel Conceptual Example 26-2: Series or parallel? (a) The lightbulbs in the figure are identical. Which configuration produces more light? (b) Which way do you think the headlights of a car are wired? Ignore change of filament resistance R with current.

  33. 26-2 Resistors in Series and in Parallel Conceptual Example 26-3: An illuminating surprise. A 100-W, 120-V lightbulb and a 60-W, 120-V lightbulb are connected in two different ways as shown. In each case, which bulb glows more brightly? Ignore change of filament resistance with current (and temperature).

  34. 26-2 Resistors in Series and in Parallel Example 26-4: Circuit with series and parallel resistors. How much current is drawn from the battery shown?

  35. 26-2 Resistors in Series and in Parallel Example 26-5: Current in one branch. What is the current through the 500-Ω resistor shown? (Note: This is the same circuit as in the previous problem.) The total current in the circuit was found to be 17 mA.

  36. 26-2 Resistors in Series and in Parallel Conceptual Example 26-6: Bulb brightness in a circuit. The circuit shown has three identical lightbulbs, each of resistance R. (a) When switch S is closed, how will the brightness of bulbs A and B compare with that of bulb C? (b) What happens when switch S is opened? Use a minimum of mathematics in your answers.

  37. 26-2 Resistors in Series and in Parallel Example 26-7: A two-speed fan. One way a multiple-speed ventilation fan for a car can be designed is to put resistors in series with the fan motor. The resistors reduce the current through the motor and make it run more slowly. Suppose the current in the motor is 5.0 A when it is connected directly across a 12-V battery. (a) What series resistor should be used to reduce the current to 2.0 A for low-speed operation? (b) What power rating should the resistor have?

  38. 26-2 Resistors in Series and in Parallel Example 26-8: Analyzing a circuit. A 9.0-V battery whose internal resistance r is 0.50 Ω is connected in the circuit shown. (a) How much current is drawn from the battery? (b) What is the terminal voltage of the battery? (c) What is the current in the 6.0-Ω resistor?

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