Copyright © 2009 Pearson Education, Inc. Chapter 24 Capacitance, Dielectrics, Electric Energy Storage

Copyright © 2009 Pearson Education, Inc. A charged capacitor stores electric energy; the energy stored is equal to the work done to charge the capacitor: 24-4 Electric Energy Storage

Copyright © 2009 Pearson Education, Inc Electric Energy Storage National Ignition Facility (NIF) Lawrence Livermore National Laboratory

Copyright © 2009 Pearson Education, Inc. NIF Laser system driven by μF capacitors which store a total of 422 MJ. They take 60 s to charge and are discharged in 400 μs. 1)What is the potential difference across each capacitor? 2)What is the power delivered during the discharge?

Copyright © 2009 Pearson Education, Inc. NIF Laser system driven by μF capacitors which store a total of 422 MJ. They take 60 s to charge and are discharged in 400 μs. 1)What is the potential difference across each capacitor? 2)What is the power delivered during the discharge? Solution: 1)U = CV 2 /2 →V = (2U/C) 1/2 →V = [2(422x10 6 )/4000/300x10 -6 ] ½ = 26.5 kV 2)P = W/t = U/t = 422x10 6 /400x10 -6 ~ W = 1000 GW! cf GW for power plant

Copyright © 2009 Pearson Education, Inc Electric Energy Storage Conceptual Example 24-9: Capacitor plate separation increased. A parallel-plate capacitor carries charge Q and is then disconnected from a battery. The two plates are initially separated by a distance d. Suppose the plates are pulled apart until the separation is 2d. How has the energy stored in this capacitor changed?

Copyright © 2009 Pearson Education, Inc. The energy density, defined as the energy per unit volume, is the same no matter the origin of the electric field: The sudden discharge of electric energy can be harmful or fatal. Capacitors can retain their charge indefinitely even when disconnected from a voltage source – be careful! 24-4 Electric Energy Storage

Copyright © 2009 Pearson Education, Inc. A dielectric is an insulator, and is characterized by a dielectric constant K. Capacitance of a parallel-plate capacitor filled with dielectric: 24-5 Dielectrics Using the dielectric constant, we define the permittivity:

Copyright © 2009 Pearson Education, Inc. Dielectric strength is the maximum field a dielectric can experience without breaking down Dielectrics

Copyright © 2009 Pearson Education, Inc Dielectrics Here are two experiments where we insert and remove a dielectric from a capacitor. In the first, the capacitor is connected to a battery, so the voltage remains constant. The capacitance increases, and therefore the charge on the plates increases as well.

Copyright © 2009 Pearson Education, Inc Dielectrics In this second experiment, we charge a capacitor, disconnect it, and then insert the dielectric. In this case, the charge remains constant. Since the dielectric increases the capacitance, the potential across the capacitor drops.

Copyright © 2009 Pearson Education, Inc. The molecules in a dielectric, when in an external electric field, tend to become oriented in a way that reduces the external field Molecular Description of Dielectrics

Copyright © 2009 Pearson Education, Inc. This means that the electric field within the dielectric is less than it would be in air, allowing more charge to be stored for the same potential. This reorientation of the molecules results in an induced charge – there is no net charge on the dielectric, but the charge is asymmetrically distributed. The magnitude of the induced charge depends on the dielectric constant: 24-6 Molecular Description of Dielectrics

Copyright © 2009 Pearson Education, Inc. Capacitor: device consisting of nontouching conductors carrying equal and opposite charge. Capacitance: Capacitance of a parallel-plate capacitor: Summary of Chapter 24

Copyright © 2009 Pearson Education, Inc. Summary of Chapter 24 Capacitors in parallel: Capacitors in series:

Copyright © 2009 Pearson Education, Inc. Energy density in electric field: A dielectric is an insulator. Dielectric constant gives ratio of total field to external field. For a parallel-plate capacitor: Summary of Chapter 24

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

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

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

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:

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

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?

ConcepTest 25.1Connect the Battery Which is the correct way to light the lightbulb with the battery? 4) all are correct 5) none are correct 1) 3) 2)

continuous connection Current can flow only if there is a continuous connection from the negative terminal through the bulb to the positive terminal. This is the case for only Fig. (3). ConcepTest 25.1Connect the Battery Which is the correct way to light the lightbulb with the battery? 4) all are correct 5) none are correct 1) 3) 2)

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

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

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

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

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 ?

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?

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

Ohm’s law is obeyed since the current still increases when V increases 1) Ohm’s law is obeyed since the current still increases when V increases Ohm’s law is not obeyed 2) Ohm’s law is not obeyed this has nothing to do with Ohm’s law 3) 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?

Ohm’s law is obeyed since the current still increases when V increases 1) Ohm’s law is obeyed since the current still increases when V increases Ohm’s law is not obeyed 2) Ohm’s law is not obeyed this has nothing to do with Ohm’s law 3) 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?

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

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

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?

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

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?

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 1) d A = 4d B d A = 2d B 2) d A = 2d B d A = d B 3) d A = d B 4) d A = 1/2d B 5) d A = 1/4d B

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 1) d A = 4d B d A = 2d B 2) d A = 2d B d A = d B 3) d A = d B 4) d A = 1/2d B 5) d A = 1/4d B

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

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

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

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

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?

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?

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

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

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

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

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

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?

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

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:.

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

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).

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 /A, I = jA, and V = E l, and substituting in Ohm’s law gives:

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.)

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

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

Copyright © 2009 Pearson Education, Inc. 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: Summary of Chapter 25

Copyright © 2009 Pearson Education, Inc. Ohmic materials have constant resistance, independent of voltage. Resistance is determined by shape and material: ρ is the resistivity. Summary of Chapter 25

Copyright © 2009 Pearson Education, Inc. Power in an electric circuit: Direct current is constant. Alternating current varies sinusoidally: Summary of Chapter 25

Copyright © 2009 Pearson Education, Inc. The average (rms) current and voltage: Relation between drift speed and current: Summary of Chapter 25