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DC Circuits

DC Circuits. Chap. 28 Exer. 5, 6, 7, 8, Exer. 9, 10, 11, 12, 17, 18, Exer. 21, 22, 23, 24, 29, 30, 31, 32, Prob. 2. Homework. EMF and Terminal Voltage Resistors in Series and in Parallel Kirchhoff’s Rules Series and Parallel EMFs; Battery Charging

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DC Circuits

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  1. DC Circuits

  2. Chap. 28 Exer. 5, 6, 7, 8, Exer. 9, 10, 11, 12, 17, 18, Exer. 21, 22, 23, 24, 29, 30, 31, 32, Prob. 2. Homework

  3. 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

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

  5. EMF and Terminal Voltage This resistance behaves as though it were in series with the emf.

  6. EMF and Terminal Voltage 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.

  7. Solution:

  8. 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.

  9. 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:

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

  11. Resistors in Series and in Parallel The voltage across each resistor is the same: The total current is the sum of the currents across each resistor: ,

  12. Resistors in Series and in Parallel This gives the reciprocal of the equivalent resistance:

  13. 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.

  14. Resistors in Series and in Parallel 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.

  15. Resistors in Series and in Parallel 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).

  16. Solution

  17. Resistors in Series and in Parallel Circuit with series and parallel resistors. How much current is drawn from the battery shown? What is the current through each of the resistor?

  18. Solution:

  19. Resistors in Series and in Parallel 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.

  20. Solution:

  21. Resistors in Series and in Parallel 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?

  22. Resistors in Series and in Parallel 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? a b d c

  23. Solution: Current drawn from EMF Current through each resistor Equivalent resistance

  24. Solution:

  25. Solution:

  26. Kirchhoff’s Rules Some circuits cannot be broken down into series and parallel connections. For these circuits we use Kirchhoff’s rules.

  27. Kirchhoff’s Rules Junction rule: The sum of currents entering a junction equals the sum of the currents leaving it.

  28. Kirchhoff’s Rules Loop rule: The sum of the changes in potential around a closed loop is zero.

  29. Kirchhoff’s Rules • Junction rule: • Loop rule:

  30. Kirchhoff’s Rules • Label each current, including its direction. • Identify unknowns. • Apply junction and loop rules; you will need as many independent equations as there are unknowns. • Solve the equations, being careful with signs. If the solution for a current is negative, that current is in the opposite direction from the one you have chosen.

  31. Kirchhoff’s Rules Using Kirchhoff’s rules. Calculate the currents I1, I2, and I3 in the three branches of the circuit in the figure.

  32. Solution:

  33. Remark:

  34. Chap. 28 Exer. 35, 36, 37, 38, Exer. 45, 46, 47, 48, Exer. 51, 52, 61, 62, Prob. 7. Chap. 29 Exer. 3, 4, 5, 6, 7, 8, Exer. 13, 14, 15, 16, Exer. 20, 21, 24, Homework

  35. Calculate the equivalent resistance:

  36. I I-I1 I1 I1-I2 I-I2 I2 I

  37. Solution: Solving the coupled equations and expressI1andI2in terms ofI, R1, R2 andR3

  38. Solution:

  39. Series and Parallel EMFs; Battery Charging EMFs in series in the same direction: total voltage is the sum of the separate voltages.

  40. Series and Parallel EMFs EMFs in series, opposite direction: total voltage is the difference, but the lower-voltage battery is charged.

  41. Series and Parallel EMFs EMFs in parallel only make sense if the voltages are the same; this arrangement can produce more current than a single emf.

  42. Battery Charging Jump starting a car. A good car battery is being used to jump start a car with a weak battery. The good battery has an emf of 12.5 V and internal resistance 0.020 Ω. Suppose the weak battery has an emf of 10.1 V and internal resistance 0.10 Ω. Each copper jumper cable is 3.0 m long and 0.50 cm in diameter, and can be attached as shown. Assume the starter motor can be represented as a resistor Rs = 0.15 Ω. Determine the current through the starter motor (a) if only the weak battery is connected to it, and (b) if the good battery is also connected.

  43. RC Circuits When the switch is closed, the capacitor will begin to charge. As it does, the voltage across it increases, and the current through the resistor decreases.

  44. Circuits Containing Resistor and Capacitor (RC Circuits) If an isolated charged capacitor is connected across a resistor, it discharges: the voltage across it decreases.

  45. Circuits Containing Resistor and Capacitor (RC Circuits) To find the voltage as a function of time, we write the equation for the voltage changes around the loop:

  46. RC Circuits For discharging process, I= -dQ/dt: At t=0,Q= Q0; therefore k=lnQ0 :

  47. RC Circuits For charging process, I= +dQ/dt: At t=0,Q= 0; therefore k=ln(CE):

  48. RC Circuits The quantity RC that appears in the exponent is called the time constant of the circuit: Another time is half-life, T1/2:

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