Chapter 24 Capacitance, Dielectrics, Electric Energy Storage

Recap:

ConcepTest 24.3cCapacitors III ConcepTest 24.3c Capacitors III C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V 1) Q 1 = Q 2 2) Q 1 > Q 2 3) Q 1 < Q 2 4) all charges are zero How does the charge Q 1 on the first capacitor (C 1 ) compare to the charge Q 2 on the second capacitor (C 2 )?

ConcepTest 24.3cCapacitors III ConcepTest 24.3c Capacitors III C 1 = 1.0  F C 3 = 1.0  F C 2 = 1.0  F 10 V Q = CVsame have V 1 > V 2 Q 1 > Q 2 We already know that the voltage across C 1 is 10 V and the voltage across both C 2 and C 3 is 5 V each. Since Q = CV and C is the same for all the capacitors, we have V 1 > V 2 and therefore Q 1 > Q 2. 1) Q 1 = Q 2 2) Q 1 > Q 2 3) Q 1 < Q 2 4) all charges are zero How does the charge Q 1 on the first capacitor (C 1 ) compare to the charge Q 2 on the second capacitor (C 2 )?

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

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

Capacitor: nontouching conductors carrying equal and opposite charge. Capacitance: Capacitance of a parallel-plate capacitor: Summary of Chapter 24

Capacitors in parallel: Capacitors in series:

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. The Electric Battery Electric Current Ohm’s Law: Resistance and Resistors Resistivity Electric Power Units of Chapter 25

Copyright © 2009 Pearson Education, Inc. Power in Household Circuits Alternating Current Microscopic View of Electric Current: Current Density and Drift Velocity Superconductivity Electrical Conduction in the Nervous System Units of Chapter 25

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. 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

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 or past a point: 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: 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? In a hydrogen atom, an electron circles a nucleus. Given that it takes a minimum of 13.6 eV to remove an electron from a hydrogen atom, what current is circling the nucleus?

Copyright © 2009 Pearson Education, Inc. Hydrogen atom

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 Thanks, Ben!

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 (R): 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 (Diode)

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. 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

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.

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

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?

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?

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 1) it decreases by a factor of 4 it decreasesby a factor of 2 2) it decreases by a factor of 2 it stays the same 3) it stays the same 4) it increasesby a factor of 2 4) it increases by a factor of 2 5) it increasesby a factor of 4 5) it increases by a factor of 4

doubledhalved Keeping the volume (= area x length) constant means that if the length is doubled, the area is halved. Since, 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 1) it decreases by a factor of 4 it decreasesby a factor of 2 2) it decreases by a factor of 2 it stays the same 3) it stays the same 4) it increasesby a factor of 2 4) it increases by a factor of 2 5) it increasesby a factor of 4 5) it increases by a factor of 4

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. 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: Resistance thermometer. A nichrome heater dissipates 500 W when the applied potential difference is 110 V and the wire temperature is 800 o C. What would the dissipation rate be if the wire temperature were held at 200 o C by immersing the wire in a bath of oil while the applied potential difference remains the same?

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: Electric light. A 100 W light bulb is plugged into a standard 120 V outlet. a) At $0.08/kW-hr, how much does it cost to have the bulb on 24 hrs/day for a 31-day month? b) What is the resistance of the bulb? c) What is the current in the bulb?

Copyright © 2009 Pearson Education, Inc. Electric light

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

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

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

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?

Questions?