![Example 23.6 Current in a parallel resistor
circuit
The three resistors of FIGURE 23.22 are connected to a
12 V battery. What current is provided by the battery?
[Insert Figure 23.22]](https://image.slidesharecdn.com/circuits-231022085023-6d4ff9ef/85/Circuits-pptx-59-320.jpg)
Circuits.pptx
- 1. CIRCUITS PREPARED BY : TYPE YOUR NAME HERE
- 2. S8FE -li - 31 Explain the advantages and disadvantages of series and parallel connections in homes
- 3. Looking Ahead: Series and Parallel Circuits • There are two basic ways to connect resistors together and capacitors together: series circuits and parallel circuits. • wired in parallel wired in series Slide 23-3
- 12. Parallel circuit
- 15. Looking Ahead: Electricity in the Body • Your nervous system works by transmitting electrical signals along axons, the long nerve fibers shown here. • You’ll learn how to understand nerve impulses in terms of the resistance, capacitance, and electric potential of individual nerve cells.
- 16. • In Section 22.5 you learned Ohm’s law, the relationship between the current through a resistor and the potential difference across it. • In this chapter, you’ll use Ohm’s law when analyzing more complex circuits consisting of multiple resistors and batteries. Slide 23-16
- 17. Rank in order, from smallest to largest, the resistances R1 to R4 of the four resistors.
- 18. The symbol shown represents a A. Battery. B. Resistor. C. Capacitor. D. Transistor.
- 19. The bulbs in the circuit below are connected . A. In series B. In parallel
- 20. Which terminal of the battery has a higher potential? A.The top terminal B.The bottom terminal
- 21. When three resistors are combined in series the total resistance of the combination is A.Greater than any of the individual resistance values. B. Less than any of the individual resistance values. C. The average of the individual resistance values.
- 22. Answer: A
- 23. In an RC circuit, what is the name of the quantity represented by the symbol ? A. The decay constant B. The characteristic time C. The time constant D. The resistive component E. The Kirchoff
- 24. Answer C
- 26. Circuit Elements and Diagrams • This is an electric circuit in which a resistor and a capacitor are connected by wires to a battery. • To understand the operation of the circuit, we do not need to know whether the wires are bent or straight, or whether the battery is to the right or left of the resistor. • The literal picture provides many irrelevant details.
- 27. Circuit Elements and Diagrams • Rather than drawing a literal picture of circuit to describe or analyze circuits, we use a more abstract picture called a circuit diagram. • A circuit diagram is a logical picture of what is connected to what. • The actual circuit may look quite different from the circuit diagram, but it will have the same logic and connections.
- 28. Circuit Elements and Diagrams • Here are the basic symbols used for electric circuit drawings:
- 29. Circuit Elements and Diagrams • Here are the basic symbols used for electric circuit drawings: Slide 23-29
- 30. Does the bulb light? A.Yes B.No C.I’m not sure.
- 31. Answer: No
- 32. Circuit Elements and Diagrams • The circuit diagram for the simple circuit is now shown. • The battery’s emf ℇ, the resistance R, and the capacitance C of the capacitor are written beside the circuit elements. • The wires, which in practice may bend and curve, are shown as straight-line connections between the circuit elements.
- 33. Kirchhoff’s Laws • Kirchhoff ’sjunction law, as we learned in Chapter 22, states that the total current into a junction must equal the total current leaving the junction. • This is a result of charge and current conservation:
- 34. Series Resistors • If we replace two resistors with a single resistor having the value Req = R1 +R2 the total potential difference across this resistor is still ℇbecause the potential difference is established by the battery.
- 35. Series Resistors • The current in the single resistor circuit is: • The single resistor is equivalent to the two series resistors in the sense that the circuit’s current and potential difference are the same in both cases. • If we have N resistors in series, their equivalent resistance is the sum of the N individual resistances:
- 36. QuickCheck The current through the 3 resistor is A. 9A B. 6A C. 5A D. 3A E. 1A
- 37. Answer: E
- 38. Potential difference of Christmas- tree mini lights A string of Christmas-tree minilights consists of 50 bulbs wired in series. What is the potential difference across each bulb when the string is plugged into a 120 V outlet?
- 39. Potential difference of Christmas- tree minilights PREPARE FIGURE 23.14 shows the minilight circuit, which has 50 bulbs in series. The current in each of the bulbs is the same because they are in series.
- 40. Potential difference of Christmas- tree minilights SOLVE Applying Kirchhoff’s loop law around the circuit, we find
- 41. The bulbs are all identical and, because the current in the bulbs is the same, all of the bulbs have the same potential difference. The potential difference across a single bulb is thus Potential difference of Christmas- tree minilights
- 42. Slid e 23- 42 ASSESS This result seems reasonable. The potential difference is “shared” by the bulbs in the circuit. Since the potential difference is shared among 50 bulbs, the potential difference across each bulb will be quite small. Potential difference of Christmas- tree minilights
- 43. Series Resistors • We compare two circuits: one with a single lightbulb, and the other with two lightbulbs connected in series. All of the batteries and bulbs are identical. • How does the brightness of the bulbs in the different circuits compare?
- 44. Series Resistors • In a circuit with one bulb, circuit A, a battery drives the current IA = ℇ/R through the bulb. • In a circuit, with two bulbs (in series) with the same resistance R, circuit B, the equivalent resistance is Req = 2R. • The current running through the bulbs in the circuit B is IB = ℇ/2R. • Since the emf from the battery and the resistors are the same in each circuit, IB = ½ IA. • The two bulbs in circuit B are equally bright, but they are dimmer than the bulb in circuit A because there is less current.
- 45. Series Resistors • A battery is a source of potential difference, not a source of current. • The battery does provide the current in a circuit, but the amount of current depends on the resistance. • The amount of current depends jointly on the battery’s emf and the resistance of the circuit attached to the battery.
- 46. Parallel Resistors • In a circuit where two bulbs are connected at both ends, we say that they are connected in parallel.
- 47. Conceptual Example 23.5 Brightness of bulbs in parallel Which lightbulb in the circuit of FIGURE 23.18 is brighter: A or B? Or are they equally bright?
- 49. ASSESS One might think that A would be brighter than B because current takes the “shortest route.” But current is determined by potential difference, and two bulbs connected in parallel have the same potential difference.
- 50. Parallel Resistors • The potential difference across each resistor in parallel is equal to the emf of the battery because both resistors are connected directly to the battery.
- 51. Parallel Resistors • The current Ibat from the battery splits into currents I1 and I2 at the top of the junction. • According to the junction law, • Applying Ohm’s law to each resistor, we find that the battery current is
- 52. Parallel Resistors • Can we replace a group of parallel resistors with a single equivalent resistor? • To be equivalent, ΔV must equal ℇand I must equal Ibat: • This is the equivalent resistance, so a single Req acts exactly the same as multiple resistors.
- 54. Parallel Resistors • How does the brightness of bulb B compare to that of bulb A? • Each bulb is connected to the same potential difference, that of the battery, so they all have the same brightness. • In the second circuit, the battery must power two lightbulbs, so it provides twice as much current.
- 55. What things about the resistors in this circuit are the same for all three? A. Current I B. Potential difference V C. Resistance R D. A and B E. B and C
- 56. Answer : B
- 57. Which resistor dissipates more power? A. The 9 resistor B. The 1 resistor C. They dissipate the same power
- 58. Answer: B
- 59. Example 23.6 Current in a parallel resistor circuit The three resistors of FIGURE 23.22 are connected to a 12 V battery. What current is provided by the battery? [Insert Figure 23.22]
- 60. Example 23.6 Current in a parallel resistor circuit (cont.) PREPARE The three resistors are in parallel, so we can reduce them to a single equivalent resistor, as in FIGURE 23.23.
- 61. “However difficult life may seem, there is always something you can do and succeed at.” ― STEPHEN HAWKING