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

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Copyright © 2009 Pearson Education, Inc. 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 The Electric Battery

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Copyright © 2009 Pearson Education, Inc. 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 dissolved The Electric Battery

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Copyright © 2009 Pearson Education, Inc. Several cells connected together make a battery, although now we refer to a single cell as a battery as well The Electric Battery

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Copyright © 2009 Pearson Education, Inc. Electric current is the rate of flow of charge through a conductor: Unit of electric current: the ampere, A: 1 A = 1 C/s Electric Current The instantaneous current is given by:

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Copyright © 2009 Pearson Education, Inc. 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! 25-2 Electric Current

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Copyright © 2009 Pearson Education, Inc 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?

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Copyright © 2009 Pearson Education, Inc Electric Current Conceptual Example 25-2: 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?

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Copyright © 2009 Pearson Education, Inc. By convention, current is defined as flowing from + to -. Electrons actually flow in the opposite direction, but not all currents consist of electrons Electric Current

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Copyright © 2009 Pearson Education, Inc. Experimentally, it is found that the current in a wire is proportional to the potential difference between its ends: 25-3 Ohm’s Law: Resistance and Resistors

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Copyright © 2009 Pearson Education, Inc. The ratio of voltage to current is called the resistance: 25-3 Ohm’s Law: Resistance and Resistors

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Copyright © 2009 Pearson Education, Inc. 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 Ohm’s Law: Resistance and Resistors

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Copyright © 2009 Pearson Education, Inc 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 ?

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Copyright © 2009 Pearson Education, Inc 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?

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Copyright © 2009 Pearson Education, Inc. Standard resistors are manufactured for use in electric circuits; they are color-coded to indicate their value and precision Ohm’s Law: Resistance and Resistors

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Copyright © 2009 Pearson Education, Inc 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.

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Copyright © 2009 Pearson Education, Inc. 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 Ohm’s Law: Resistance and Resistors

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Copyright © 2009 Pearson Education, Inc. 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 Resistivity

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Copyright © 2009 Pearson Education, Inc Resistivity This table gives the resistivity and temperature coefficients of typical conductors, semiconductors, and insulators.

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Copyright © 2009 Pearson Education, Inc 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?

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Copyright © 2009 Pearson Education, Inc 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?

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Copyright © 2009 Pearson Education, Inc. For any given material, the resistivity increases with temperature: Semiconductors are complex materials, and may have resistivities that decrease with temperature Resistivity

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Copyright © 2009 Pearson Education, Inc Resistivity Example 25-7: Resistance thermometer. The variation in electrical resistance with temperature can be used to make precise temperature 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?

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Copyright © 2009 Pearson Education, Inc. Power, as in kinematics, is the energy transformed by a device per unit time: 25-5 Electric Power or

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Copyright © 2009 Pearson Education, Inc. The unit of power is the watt, W. For ohmic devices, we can make the substitutions: 25-5 Electric Power

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Copyright © 2009 Pearson Education, Inc Electric Power Example 25-8: Headlights. Calculate the resistance of a 40-W automobile headlight designed for 12 V.

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Copyright © 2009 Pearson Education, Inc. 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 Electric Power

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Copyright © 2009 Pearson Education, Inc 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?

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Copyright © 2009 Pearson Education, Inc 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.

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Copyright © 2009 Pearson Education, Inc. 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 Power in Household Circuits

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Copyright © 2009 Pearson Education, Inc. Fuses are one-use items – if they blow, the fuse is destroyed and must be replaced Power in Household Circuits

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Copyright © 2009 Pearson Education, Inc. Circuit breakers, which are now much more common in homes than they once were, are switches that will open if the current is too high; they can then be reset Power in Household Circuits

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Copyright © 2009 Pearson Education, Inc Power in Household Circuits Example 25-11: Will a fuse blow? Determine the total current drawn by all the devices in the circuit shown.

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Copyright © 2009 Pearson Education, Inc Power in Household Circuits Conceptual Example 25-12: A dangerous extension cord. Your 1800-W portable electric heater is too far from your desk to warm your feet. Its cord is too short, so you plug it into an extension cord rated at 11 A. Why is this dangerous?

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Copyright © 2009 Pearson Education, Inc. Current from a battery flows steadily in one direction (direct current, DC). Current from a power plant varies sinusoidally (alternating current, AC) Alternating Current

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Copyright © 2009 Pearson Education, Inc. The voltage varies sinusoidally with time: as does the current: 25-7 Alternating Current,,

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Copyright © 2009 Pearson Education, Inc. Multiplying the current and the voltage gives the power: 25-7 Alternating Current

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Copyright © 2009 Pearson Education, Inc. Usually we are interested in the average power: 25-7 Alternating Current.

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Copyright © 2009 Pearson Education, Inc. The current and voltage both have average values of zero, so we square them, take the average, then take the square root, yielding the root-mean-square (rms) value: 25-7 Alternating Current

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Copyright © 2009 Pearson Education, Inc Alternating Current Example 25-13: Hair dryer. (a) Calculate the resistance and the peak current in a 1000-W hair dryer connected to a 120-V line. (b) What happens if it is connected to a 240-V line in Britain?

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Copyright © 2009 Pearson Education, Inc. 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 Microscopic View of Electric Current: Current Density and Drift Velocity

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Copyright © 2009 Pearson Education, Inc 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:.

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Copyright © 2009 Pearson Education, Inc. This drift speed is related to the current in the wire, and also to the number of electrons per unit volume: 25-8 Microscopic View of Electric Current: Current Density and Drift Velocity and

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Copyright © 2009 Pearson Education, Inc 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).

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Copyright © 2009 Pearson Education, Inc 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 l / l A, I = jA, and V = E l, and substituting in Ohm’s law gives:

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Copyright © 2009 Pearson Education, Inc 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.)

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Copyright © 2009 Pearson Education, Inc. In general, resistivity decreases as temperature decreases. Some materials, however, have resistivity that falls abruptly to zero at a very low temperature, called the critical temperature, T C Superconductivity

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Copyright © 2009 Pearson Education, Inc. Experiments have shown that currents, once started, can flow through these materials for years without decreasing even without a potential difference. Critical temperatures are low; for many years no material was found to be superconducting above 23 K. Since 1987, new materials have been found that are superconducting below 90 K, and work on higher temperature superconductors is continuing Superconductivity

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Copyright © 2009 Pearson Education, Inc. The human nervous system depends on the flow of electric charge. The basic elements of the nervous system are cells called neurons. Neurons have a main cell body, small attachments called dendrites, and a long tail called the axon Electrical Conduction in the Nervous System

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Copyright © 2009 Pearson Education, Inc. Signals are received by the dendrites, propagated along the axon, and transmitted through a connection called a synapse Electrical Conduction in the Nervous System

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Copyright © 2009 Pearson Education, Inc. This process depends on there being a dipole layer of charge on the cell membrane, and different concentrations of ions inside and outside the cell Electrical Conduction in the Nervous System

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Copyright © 2009 Pearson Education, Inc. This applies to most cells in the body. Neurons can respond to a stimulus and conduct an electrical signal. This signal is in the form of an action potential Electrical Conduction in the Nervous System

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Copyright © 2009 Pearson Education, Inc. The action potential propagates along the axon membrane Electrical Conduction in the Nervous System

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Copyright © 2009 Pearson Education, Inc. Review Questions

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Ohm’s law is obeyed since the current still increases when V increases A) Ohm’s law is obeyed since the current still increases when V increases Ohm’s law is not obeyed B) Ohm’s law is not obeyed this has nothing to do with Ohm’s law C) this has nothing to do with Ohm’s law ConcepTest 25.2Ohm’s Law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude?

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Ohm’s law is obeyed since the current still increases when V increases A) Ohm’s law is obeyed since the current still increases when V increases Ohm’s law is not obeyed B) Ohm’s law is not obeyed this has nothing to do with Ohm’s law C) this has nothing to do with Ohm’s law V = IR linear Ohm’s law, V = IR, states that the relationship between voltage and current is linear. Thus, for a conductor that obeys Ohm’s law, the current must double when you double the voltage. ConcepTest 25.2Ohm’s Law You double the voltage across a certain conductor and you observe the current increases three times. What can you conclude? Follow-up: Where could this situation occur?

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ConcepTest 25.3aWires I Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? d A = 4d B A) d A = 4d B d A = 2d B B) d A = 2d B d A = d B C) d A = d B D) d A = 1/2d B E) d A = 1/4d B

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area is less arearadiussquared diameter of A must be two times less than the diameter of B The resistance of wire A is greater because its area is less than wire B. Since area is related to radius (or diameter) squared, the diameter of A must be two times less than the diameter of B. ConcepTest 25.3aWires I Two wires, A and B, are made of the same metal and have equal length, but the resistance of wire A is four times the resistance of wire B. How do their diameters compare? d A = 4d B A) d A = 4d B d A = 2d B B) d A = 2d B d A = d B C) d A = d B D) d A = 1/2d B E) d A = 1/4d B

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ConcepTest 25.3bWires II A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? it decreasesby a factor of 4 A) it decreases by a factor of 4 it decreasesby a factor of 2 B) it decreases by a factor of 2 it stays the same C) it stays the same D) it increasesby a factor of 2 D) it increases by a factor of 2 E) it increasesby a factor of 4 E) it increases by a factor of 4

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doubledhalved Keeping the volume (= area x length) constant means that if the length is doubled, the area is halved. This increases the resistance by a factor of 4. ConcepTest 25.3bWires II A wire of resistance R is stretched uniformly (keeping its volume constant) until it is twice its original length. What happens to the resistance? it decreasesby a factor of 4 A) it decreases by a factor of 4 it decreasesby a factor of 2 B) it decreases by a factor of 2 it stays the same C) it stays the same D) it increasesby a factor of 2 D) it increases by a factor of 2 E) it increasesby a factor of 4 E) it increases by a factor of 4

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Copyright © 2009 Pearson Education, Inc. Ch. 25 Homework Finish reading Ch. 25. Begin looking over Ch. 26 Group problems #’s 6, 14, 18, 40 HW Problems #’s 5, 9, 13, 15, 19, 25, 35, 39, 51

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