# Chapter 25 Electric Currents and. Copyright 2009 Pearson Education, Inc.

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1 Chapter 25 Electric Currents and Resistance

2 25-1 The Electric Battery Volta discovered that electricity could be created if dissimilar metals were connected by a conductive solution called an electrolyte. This is a simple electric cell.

3 25-1 The Electric Battery A battery transforms chemical energy into electrical energy. Chemical reactions within the cell create a potential difference between the terminals by slowly dissolving them. This potential difference can be maintained even if a current is kept flowing, until one or the other terminal is completely l dissolved. d

4 25-1 The Electric Battery Several cells connected together make a battery, although now we refer to a single cell as a battery as well.

5 25-2 Electric Current Electric current is the rate of flow of charge through a conductor: The instantaneous current is given by: Unit of electric current: the ampere, A: 1 A = 1 C/s.

6 25-2 Electric Current A complete circuit is one where current can flow all the way around. Note that the schematic drawing doesn t look much like the physical circuit!

7 25-2 Electric Current Example 25-1: Current is flow of charge. A steady current of 2.5 A exists in a wire for 4.0 min. (a) How much total charge passed by a given point in the circuit during those 4.0 min? (b) How many electrons would this be? Solution p654

8 25-2 Electric Current Conceptual Example 25-2: 2 How to connect a battery. What is wrong with each of the schemes shown for lighting a flashlight bulb with a flashlight battery and a single wire? Solution p655

9 25-2 Electric Current By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons.

10 25-3 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:

11 25-3 Ohm s Law: Resistance and Resistors The ratio of voltage to current is called the resistance:

12 25-3 Ohm s Law: Resistance and Resistors In many conductors, the resistance is independent of the voltage; this relationship is called Ohm s law. Materials that do not follow Ohm s law are called nonohmic. Unit of resistance: the ohm, Ω: 1 Ω = 1 V/A.

13 25-3 Ohm s Law: Resistance and Resistors Conceptual Example 25-3: Current and potential. Current I enters a resistor R as shown. (a) Is the potential higher at point A or at point B? (b) Is the current greater at point A or at point B? Solution p656

14 25-3 Ohm s Law: Resistance and Resistors Example 25-4: Flashlight bulb resistance. A small flashlight bulb draws 300 ma from its 1.5-V battery. (a) What is the resistance of the bulb? (b) If the battery becomes weak and the voltage drops to 1.2 V, how would the current change? Solution p657

15 25-3 Ohm s Law: Resistance and Resistors Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision. i

16 25-3 Ohm s Law: Resistance and Resistors This is the standard resistor color code. Note that the colors from red to violet are in the order they appear in a rainbow.

17 25-3 Ohm s Law: Resistance and Some clarifications: Resistors 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.

18 25-4 Resistivity The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area: The constant ρ, the resistivity, is characteristic of the material.

19 25-4 Resistivity This table gives the resistivity and temperature coefficients of typical conductors, semiconductors, and insulators.

20 25-4 Resistivity Example 25-5: Speaker wires. Suppose you want to connect your stereo to remote speakers. (a) If each wire must be 20 m long, what diameter copper wire should you use to keep the resistance less than 0.10 Ω per wire? (b) If the current to each speaker is 4.0 A, what is the potential difference, or voltage drop, across each wire? Solution p659

21 25-4 Resistivity Conceptual Example 25-6: Stretching changes resistance. Suppose a wire of resistance R could be stretched uniformly until it was twice its original length. What would happen to its resistance? Solution p659

22 25-4 Resistivity For any given material, the resistivity increases with temperature: Semiconductors are complex materials, and may have resistivities that decrease with temperature.

23 25-4 Resistivity Example 25-7: Resistance thermometer. The variation in electrical resistance with temperature can be used to make precise temperature t measurements. Platinum is commonly used since it is relatively free from corrosive effects and has a high melting point. Suppose at 20.0 C the resistance of a platinum resistance thermometer is Ω. When placed in a particular solution, the resistance is Ω. What is the temperature of this solution? Solution p660

24 25-5 Electric Power Power, as in kinematics, is the energy transformed by a device per unit time: or

25 25-5 Electric Power The unit of power is the watt, W. For ohmic devices, we can make the substitutions:

26 25-5 Electric Power Example 25-8: Headlights. Calculate the resistance of a 40-W automobile headlight designed for 12 V. Solution p661

27 25-5 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: 1 kwh = (1000 W)(3600 s) = 3.60 x 10 6 J.

28 25-5 Electric Power Example 25-9: Electric heater. An electric heater draws a steady 15.0 A on a 120-V line. How much power does it require and how much does it cost per month (30 days) if it operates 3.0 h per day and the electric company charges 9.2 cents per kwh? Solution p661

29 25-5 Electric Power Example 25-10: Lightning bolt. Lightning is a spectacular example of electric current in a natural phenomenon. There is much variability to lightning bolts, but a typical event can transfer 10 9 J of energy across a potential difference of perhaps 5 x 10 7 V during a time interval of about 0.2 s. Use this information to estimate (a) the total amount of charge transferred between cloud and ground, (b) the current in the lightning bolt, and (c) the average power delivered over the 0.2 s. Solution p662

30 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.

31 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:.

32 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

33 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). Solution p667

34 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 ll/a, I = ja, and V = El l, and substituting in Ohm s law gives:

35 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 10 5 A/m 2.) Solution p668

36 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:

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

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

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