Chapter 21 Electric Current and Direct- Current Circuits

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1 Chapter 21 Electric Current and Direct- Current Circuits

2 Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power in Electric Circuits Resistors in Series and Parallel Kirchhoff s Rules Circuits Containing Capacitors RC Circuits Ammeters and Voltmeters

3 HW # 5 Pg : # 7, 8, 11, 19, 22, 28, 32, 44, 49, 73, 78 PHYS Due on Thursday, Oct. 10 PHYS Due on Thursday, Oct. 10

4 Practical resistors:

5 Example # 4 When a potential difference of 18 V is applied to a given wire, it conducts 0.35 A of current. What is the resistance of the wire?

6 Resistance and Ohm s Law Two wires of the same length and diameter will have different resistances if they are made of different materials. This property of a material is called the resistivity.

7 Resistance and Ohm s Law The difference between insulators, semiconductors, and conductors can be clearly seen in their resistivities:

8 Resistance and Ohm s Law In general, the resistance of materials goes up as the temperature goes up, due to thermal effects. This property can be used in thermometers. Resistivity decreases as the temperature decreases, but there is a certain class of materials called superconductors in which the resistivity drops suddenly to zero at a finite temperature, called the critical temperature T C.

9 Example # 5 Nichrome is a nickel chromium alloy used in heating applications like electric toasters, because it has a relatively high resistivity and heats up when current passes through it. Suppose you have a nichrome wire 0.20 mm in diameter and 75 cm long. ( a ) What s its resistance? ( b) Find the current when a potential difference of 120 V is connected across the wire s ends.

10 Energy and Power in Electric Circuits When a charge moves across a potential difference, its potential energy changes: Therefore, the power it takes to do this is

11 Energy and Power in Electric Circuits In materials for which Ohm s law holds, the power can also be written: This power mostly becomes heat inside the resistive material.

12 Example # 6 (Your turn) Consider a 60 W light bulb, connected to a 120 V voltage source. What is the current passing through the wire in the bulb? (A) 0.5 A (B) 1.0 A (C) 2.0 A (D) 240 A What is the resistance of the wire in the bulb? (A) 0.5 W (B) 1.0 W (C) 2.0 W (D) 240 W

13 What is the current passing through the wire in the bulb? A A A A

14 What is the resistant of the wire in the bulb? A A A A

15 Conceptual Checkpoint 21-2 A battery that produces a potential difference V is connected to a 5-W lightbulb. Later the 5-W lightbult is replaced with a 10- W lightbulb. (a) In which case does the battery supply more current? W W

16 Conceptual Checkpoint 21-2 A battery that produces a potential difference V is connected to a 5-W lightbulb. Later the 5-W lightbult is replaced with a 10- W lightbulb. (b) Which lightbulb has the greater resistance? W W

17 Example # 7 pb. # 29 a) Find the power dissipated in a 25-Ω electric heater connected to a 120- V outlet kw kw kw kw

18 Energy Use: Energy and Power in Electric Circuits When the electric company sends you a bill, your usage is quoted in kilowatt-hours (kwh). They are charging you for energy use, and kwh are a measure of energy.

19 Example # 8 Electric utilities measure energy in kilowatt-hours (kwh), where 1 kwh is the energy consumed if you use energy at the rate of 1 kw for 1 hour. If your monthly electric bill (30 days) is $100 and you pay 12.5c/kWh, what s your home s average power consumption and average current, assuming a 240-V potential difference between the wires supplying your home? kw kw kw kw

20 Example # 8 Electric utilities measure energy in kilowatt-hours (kwh), where 1 kwh is the energy consumed if you use energy at the rate of 1 kw for 1 hour. If your monthly electric bill (30 days) is $100 and you pay 12.5c/kWh, what s your home s average power consumption and average current, assuming a 240-V potential difference between the wires supplying your home? Response for 2 nd question A A A A

21 Example # 9 Several male students in the same dorm room want to dry their hair. Having taken PHYS 1402 at UTPA, they have set their hair dryers to the low, 1000-W settings. Assuming a standard 120-V how many hair dryers can they operate simultaneously without tripping the 20-A circuit breaker? A A A A

22 Resistors in Series Resistors connected end to end are said to be in series. They can be replaced by a single equivalent resistance without changing the current in the circuit.

23 Resistors in Series Since the current through the series resistors must be the same in each, and the total potential difference is the sum of the potential differences across each resistor, we find that the equivalent resistance is:

24 Resistors in Series The same current ( I ) must flow through each of the resistors: I eq = I 1 = I 2 = I 3 Total potential difference from point A to point B must be the emf of the battery ε V eq = ε = V 1 + V 2 + V 3. ε = I R eq

25 Resistors in Series

26 Example # 10 Two resistors, one having half the resistance of the other, are connected to a battery as shown on the white board. What is the voltage across the bigger resistor? 1. A 2. B 3. C 4. D V b V b 3V b 2V b / 2 / 3 / 2 / 3

27 Example # 11 Two resistors, one having half the resistance of the other, are connected to an emf battery as shown on the board. What is the emf of the battery? 1. A 2. B 3. C 4. D IR / 2 IR / 3 3IR / 2 2IR / 3

28 Resistors Parallel Resistors are in parallel when they are across the same potential difference; they can again be replaced by a single equivalent resistance:

29 Resistors in Parallel Using the fact that the potential difference across each resistor is the same, and the total current is the sum of the currents in each resistor, we find: Note that this equation gives you the inverse of the resistance, not the resistance itself!

30 Resistors in Parallel The potential difference across each resistor will be the same. V eq = ε = V 1 = V 2 = V 3 The equivalent current will be the sum of all the currents. I eq = I 1 + I 2 + I 3

31 Example # 12 Two resistors are connected ( a ) in parallel, and ( b ) in series, to a 24.0 V battery. See the diagraph on the white board. What is the current through each resistor and what is the equivalent resistance of each circuit?

32 Resistors Parallel If a circuit is more complex, start with combinations of resistors that are either purely in series or in parallel. Replace these with their equivalent resistances; as you go on you will be able to replace more and more of them.

33 Kirchhoff s Rules More complex circuits cannot be broken down into series and parallel pieces. For these circuits, Kirchhoff s rules are useful. The junction rule is a consequence of charge conservation; the loop rule is a consequence of energy conservation.

34 Kirchhoff s Rules The junction rule: At any junction, the current entering the junction must equal the current leaving it.

35 Kirchhoff s Rules The loop rule: The algebraic sum of the potential differences around a closed loop must be zero (it must return to its original value at the original point).

36 Using Kirchhoff s rules: Kirchhoff s Rules The variables for which you are solving are the currents through the resistors. You need as many independent equations as you have variables to solve for. You will need both loop and junction rules.

37 Circuits Containing Capacitors Capacitors can also be connected in series or in parallel. When capacitors are connected in parallel, the potential difference across each one is the same.

38 21-6 Circuits Containing Capacitors Therefore, the equivalent capacitance is the sum of the individual capacitances:

39 21-6 Circuits Containing Capacitors Capacitors connected in series do not have the same potential difference across them, but they do all carry the same charge. The total potential difference is the sum of the potential differences across each one.

40 21-6 Circuits Containing Capacitors Therefore, the equivalent capacitance is Note that this equation gives you the inverse of the capacitance, not the capacitance itself! Capacitors in series combine like resistors in parallel, and vice versa.

41 21-7 RC Circuits In a circuit containing only batteries and capacitors, charge appears almost instantaneously on the capacitors when the circuit is connected. However, if the circuit contains resistors as well, this is not the case.

42 21-7 RC Circuits Using calculus, it can be shown that the charge on the capacitor increases as: Here, τ is the time constant of the circuit: And is the final charge on the capacitor, Q.

43 21-7 RC Circuits Here is the charge vs. time for an RC circuit:

44 21-7 RC Circuits It can be shown that the current in the circuit has a related behavior:

45 21-8 Ammeters and Voltmeters An ammeter is a device for measuring current, and a voltmeter measures voltages. The current in the circuit must flow through the ammeter; therefore the ammeter should have as low a resistance as possible, for the least disturbance.

46 21-8 Ammeters and Voltmeters A voltmeter measures the potential drop between two points in a circuit. It therefore is connected in parallel; in order to minimize the effect on the circuit, it should have as large a resistance as possible.

47 Summary of Chapter 21 Electric current is the flow of electric charge. Unit: ampere 1 A = 1 C/s A battery uses chemical reactions to maintain a potential difference between its terminals. The potential difference between battery terminals in ideal conditions is the emf. Work done by battery moving charge around circuit:

48 Summary of Chapter 21 Direction of current is the direction positive charges would move. Ohm s law: Relation of resistance to resistivity: Resistivity generally increases with temperature. The resistance of a superconductor drops suddenly to zero at the critical temperature, T C.

49 Summary of Chapter 21 Power in an electric circuit: If the material obeys Ohm s law, Energy equivalent of one kilowatt-hour: Equivalent resistance for resistors in series:

50 Summary of Chapter 21 Inverse of the equivalent resistance of resistors in series: Junction rule: All current that enters a junction must also leave it. Loop rule: The algebraic sum of all potential charges around a closed loop must be zero.

51 Summary of Chapter 21 Equivalent capacitance of capacitors connected in parallel: Inverse of the equivalent capacitance of capacitors connected in series:

52 Charging a capacitor: Summary of Chapter 21 Discharging a capacitor:

53 Summary of Chapter 21 Ammeter: measures current. Is connected in series. Resistance should be as small as possible. Voltmeter: measures voltage. Is connected in parallel. Resistance should be as large as possible.

Lecture Outline Chapter 21. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc.

Lecture Outline Chapter 21. Physics, 4 th Edition James S. Walker. Copyright 2010 Pearson Education, Inc. Lecture Outline Chapter 21 Physics, 4 th Edition James S. Walker Chapter 21 Electric Current and Direct- Current Circuits Units of Chapter 21 Electric Current Resistance and Ohm s Law Energy and Power