Physics 213 General Physics Lecture 5

2 Last Meeting: Capacitance Today: Current and Resistance

Energy Stored in a Capacitor Energy stored = ½ Q ΔV From the definition of capacitance, this can be rewritten in different forms

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Quiz: The plates of a connected parallel-plate capacitor of capacitance C are brought together to one-third their original separation. The energy stored is now (a) W/9 (b) W/3 (c) 3W (d) 9W Answer: c

QUIZ A fully charged parallel-plate capacitor remains connected to a battery while you slide a dielectric between the plates. Do the following quantities increase, decrease, or stay the same? (a) C; (b) Q; (c) E between the plates; (d)  V.

QUIZ (a) C increases (b) Q increases (c) E stays the same (d)  V remains the same

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Charge Carrier Motion in a Conductor The zig-zag black line represents the motion of a charge carrier in a conductor The net drift speed is small The sharp changes in direction are due to collisions The net motion of electrons is opposite the direction of the electric field

Charge Carrier Motion in a Conductor The drift speed V d is small (~1meter/hour) The fermi speed V f is very fast! Due to quantum mechanics of electrons. (~10 6 meters/second) Charge rearrangements and signals travel near speed of light (~10 8 meters/second)

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19 Variety of Resistors

Temperature Variation of Resistivity For most metals, resistivity increases with increasing temperature With a higher temperature, the metal’s constituent atoms vibrate with increasing amplitude The electrons find it more difficult to pass through the atoms

Temperature Variation of Resistivity, cont For most metals, resistivity increases approximately linearly with temperature over a limited temperature range ρ is the resistivity at some temperature T ρ o is the resistivity at some reference temperature T o T o is usually taken to be 20° C  is the temperature coefficient of resistivity

22 Energy is turned to heat (random motion)

Electrical Energy and Power The rate at which the energy is lost is the power From Ohm’s Law, alternate forms of power are

Electrical Energy and Power, cont

Electrical Energy and Power, final The SI unit of power is Watt (W) I must be in Amperes, R in ohms and  V in Volts The unit of energy used by electric companies is the kilowatt-hour This is defined in terms of the unit of power and the amount of time it is supplied 1 kWh = 3.60 x 10 6 J