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CIRCUITS

CIRCUITS. The Electric Battery. A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals This potential difference can be maintained even if a current is kept flowing. The Electric Battery.

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CIRCUITS

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  1. CIRCUITS

  2. The Electric Battery A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals This potential difference can be maintained even if a current is kept flowing.

  3. The Electric Battery Several cells connected together make a battery, although now we refer to a single cell as a battery as well.

  4. Ohm’s Law: Resistance and Resistors Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends:

  5. Ohm’s Law: Resistance and Resistors The ratio of voltage to current is called the resistance: I= V/R

  6. Ohm’s Law: Resistance and Resistors • Some clarifications: • Batteries maintain a (nearly) constant potential difference; the current varies. • Resistance is a property of a material or device. • Current is not a vector but it does have a direction. • Current and charge do not get used up. Whatever charge goes in one end of a circuit comes out the other end.

  7. A battery is connected to a resistor. As charge flows, the chemical energy of the battery is dissipated as • current. • voltage. • charge. • thermal energy. Slide 22-10

  8. Answer • A battery is connected to a resistor. As charge flows, the chemical energy of the battery is dissipated as • current. • voltage. • charge. • thermal energy. Slide 22-11

  9. A battery is connected to a resistor. Increasing the resistance of the resistor will • increase the current in the circuit. • decrease the current in the circuit. • not affect the current in the circuit. Slide 22-8

  10. Answer • A battery is connected to a resistor. Increasing the resistance of the resistor will • increase the current in the circuit. • decrease the current in the circuit. • not affect the current in the circuit. Slide 22-9

  11. Electric Power Power, as in kinematics, is the energy transformed by a device per unit time:

  12. Energy and Power in Resistors Slide 22-31

  13. Electric Power The unit of power is the watt, W. For ohmic devices, we can make the substitutions:

  14. Electric Power The unit of power is the watt, W. For ohmic devices, we can make the substitutions:

  15. Electric Power What you pay for on your electric bill is not power, but energy – the power consumption multiplied by the time. We have been measuring energy in joules, but the electric company measures it in kilowatt-hours, kWh.

  16. Power in Household Circuits The wires used in homes to carry electricity have very low resistance. However, if the current is high enough, the power will increase and the wires can become hot enough to start a fire. To avoid this, we use fuses or circuit breakers, which disconnect when the current goes above a predetermined value.

  17. Checking Understanding • A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now • 1.0 W • 2.0 W • 3.0 W • 4.0 W Slide 22-32

  18. Answer • A resistor is connected to a 3.0 V battery; the power dissipated in the resistor is 1.0 W. The battery is traded for a 6.0 V battery. The power dissipated by the resistor is now • 1.0 W • 2.0 W • 3.0 W • 4.0 W Slide 22-33

  19. Problem An electric blanket has a wire that runs through the interior. A current causes energy to be dissipated in the wire, warming the blanket. A new, low-voltage electric blanket is rated to be used at 18 V. It dissipates a power of 82 W. What is the resistance of the wire that runs through the blanket? Slide 22-34

  20. Problem • Standard electric outlets in the United States run at 120 V; in England, outlets are 230 V. An electric kettle has a coiled wire inside that dissipates power when it carries a current, warming the water in the kettle. A kettle designed for use in England carries 13 A when connected to a 230 V outlet. • What is the resistance of the wire? • What power is dissipated when the kettle is running? • The kettle can hold 1.7 L of water. Assume that all power goes to heating the water. How long will it take for the kettle to heat the water from 20ºC to 100ºC? Slide 22-37

  21. Question A set of lightbulbs have different rated voltage and power, as in the table below. Which one has lowest resistance? Bulb Rated voltage Rated power A 10 V 1 W B 8 V 1 W C 12 V 2 W D 6 V 2 W E 3 V 3 W Slide 22-41

  22. Answer 2. A set of lightbulbs have different rated voltage and power, as in the table below. Which one has lowest resistance? Bulb Rated voltage Rated power A 10 V 1 W B 8 V 1 W C 12 V 2 W D 6 V 2 W E 3 V 3 W Slide 22-42

  23. Problem • How much time does it take for 1.0 C to flow through each of the following circuit elements? • A 60 W reading light connected to 120 V. • A 60 W automobile headlamp connected to 12 V. Slide 22-47

  24. Resistors in Series A series connection has a single path from the battery, through each circuit element in turn, then back to the battery.

  25. Resistors in Series 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. V = I ( R1+ R2 + R3)

  26. Resistors in Series From this we get the equivalent resistance (that single resistance that gives the same current in the circuit).

  27. Resistors in Parallel A parallel connection splits the current; the voltage across each resistor is the same:

  28. Resistors in Parallel At A I = I1 + I2 + I3

  29. Resistors in Parallel The total current is the sum of the currents across each resistor:

  30. Resistors in Parallel This gives the reciprocal of the equivalent resistance: For two resistors in parallel 1/Req = 1/R + 1/R =2/R Req = R/2 Twice as much current can flow

  31. Resistors in Parallel An analogy using water may be helpful in visualizing parallel circuits: The height h is same for both (e.g. equal V). Twice as much water will flow with both open. Twice as much current will flow with 2 R’s parallel.

  32. Review • Exam on Monday • Covers all lectures, HW and readings from Wed. Oct 13 until Wed. Nov.3 • Only MC questions from Chemistry material (Brown readings)

  33. Review • An electron volt (eV) is a unit of • A) Charge • B) current • C) potential • D) energy • E) capacitance

  34. Review • An electron volt (eV) is a unit of • A) Charge • B) current • C) potential • D) energy • E) capacitance • An electron volt is the energy change when a particle of charge e moves through a potential difference of 1 V • 1 eV = 1.6 x 10-19J

  35. Review • What is electric potential? • Analogy- Escalator • How much work do we do • when we send boxes of • mass m1, m2, m3,… up • m1gh+ m2gh+ m3gh +… • Easier to sum the masses • m1 + m2+ m3+ .. And then • multiply by gh

  36. Review Similar for charges. Just as a mass gains or loses gravitational PE as It is raised or lowered an electric charge gains or loses electrical PE as it moves from a region of one potential V1 to another of V2 A charge q changes its energy by q( V2-V1) A charge e passing through a 6V Battery changes its energy by 6eV

  37. Review • Placing charges in a region changes the space in that region. • If the Moon were only 240 miles from E instead of 240,000 we things would be different. • Placing charge + here changes space here. This change is recorded as E

  38. Example Problems There is a current of 1.0 A in the circuit below. What is the resistance of the unknown circuit element? Slide 23-24

  39. Example Problems What is the current out of the battery? Slide 23-24

  40. Questions • In the circuit below, the switch is initially open and bulbs A and B are of equal brightness. When the switch is closed, what happens to the brightness of the two bulbs? • The brightness of the bulbs is not affected. • Bulb A becomes brighter, bulb B dimmer. • Bulb B becomes brighter, bulb A dimmer. • Both bulbs become brighter. Slide 23-45

  41. Answer • In the circuit below, the switch is initially open and bulbs A and B are of equal brightness. When the switch is closed, what happens to the brightness of the two bulbs? • The brightness of the bulbs is not affected. • Bulb A becomes brighter, bulb B dimmer. • Bulb B becomes brighter, bulb A dimmer. • Both bulbs become brighter. Slide 23-46

  42. Kirchhoff’s Rules Some circuits cannot be broken down into series and parallel connections.

  43. Kirchhoff’s Junction Law Slide 23-15

  44. Kirchhoff’s Rules For these circuits we use Kirchhoff’s rules. Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it. At a I3 = I1 + I2 At d I1 + I2 = I3

  45. Checking Understanding • The diagram below shows a segment of a circuit. What is the current in the 200 resistor? • 0.5 A • 1.0 A • 1.5 A • 2.0 A • There is not enough information to decide. Slide 23-18

  46. Answer • The diagram below shows a segment of a circuit. What is the current in the 200 resistor? • 0.5 A • 1.0 A • 1.5 A • 2.0 A • There is not enough information to decide. Slide 23-19

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