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Lecture 7 020910 rev with notes

# Lecture 7 020910 rev with notes - Lecture 7 February 9 2010...

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Lecture 7 February 9, 2010 Current and Resistance

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q -q q' q q -q' -q -q V V V V' In 1837 Michael Faraday investigated what happens to the capacitance of a capacitor when the gap between the plates is completely filled with an insulator (a.k.a. dielectri C Capacitor with a dielectric c) Faraday discovered that the new capacitance is given by : Here is the capacitance before the insertion of the dielectric between the plates. The factor is known as the dielectric co air air C C C nstant of the material. Faraday's experiment can be carried out in two ways: With the voltage across the plates remaining constant In this case a battery remains connected to the plates . This is V 1. shown in fig.a With the charge of the plates remaining constant. In this case the plates are isolated from the battery This is shown in fig.b q 2. air CC (25 - 15)
22 The work spent to charge a capacitor is stored in the form of potential energy that can be retrieved when is capacitor is discharged. Thus W UW q CV qV U C Potential energy stored in a capacitor 2 We can ask the question: where is the potential energy of a charged capacitor stored? The answer is counter intuitive. The energy is stored in the space between the capacitor plate Energy density s where a uniform electric field / is generated by the capacitor charges. In other words the electric field can store energy in empty space! E V d q CV U C  - - - - - + + + + + q -q d E A A We define as energy densiry (symbol ) the potential energy per unit volume. The volume between the plates is: where is the plate area Thus the energy density 2 2 2 o U uu V V V Ad A U CV V V u Ad Ad Ad d 2 2 This result, derived for the parallel plate capacitor holds in general 2 o E  2 2 o E u (25 - 14)

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The space between the plates of an isolated parallel-plate capacitor is filled by a slab of insulator with dielectric constant K . The two plates of the capacitor have charges Q and - Q . You pull out the dielectric slab. If the charges on the plates do not change, how does the energy U in the capacitor change when you remove the slab? 1 2 3 0% 0% 0% 1. It increases. 2. It decreases. 3. It remain the same.

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New Concepts: Electric current Electric current density vector Drift speed of the electrons Electric Resistance and resistivity of a conductor Ohm’s law Power in electric circuits
Consider the conductor shown in fig.a.

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Lecture 7 020910 rev with notes - Lecture 7 February 9 2010...

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