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Content Metal and Current
Metal and CurrentMetal is shiny, smooth, malleable, carry current:conduct electricity. 𝑃=𝐼𝑉=𝐼^{2}𝑅. Nonzero resistance. Wires radiate power away as heat. Electrons scatter off lattice, and lose energy. Reducing R is the target. Resistivity 𝜌=𝑅𝐴and lower 𝑇→smaller 𝜌→smaller power loss. SuperconductorSuperconductor have R=0. Carry current perfectly. Do not lose energy. Current in a loop will run forever. Expel magnetic fields (Meissner effect).ParticlesTwo kinds of particles:
Bosons can occupy the same space at the same time. Photons are bosons, e.g. lasers. Helium is a boson →superfluidity. Bose CondensationAt low temperature, bosons flock to the lowest level. Very stable state. Dissipationless flow. superfluidity, e.g. helium. Superconductivity, most metals do this at low 𝑇.SuperconductivityPair electrons→form bosons. Bosons condense into the lowest energy state. Lowest energy state cannot lose energy→electron pairs cannot dissipate energy. Dissipationless current flow. Lowest energy state cannot dissipate energy. That is excited atom release a photon to decrease the energy. While less excite atom release a photon to ground state. Atom in ground state cannot lose anymore energy→Quantum stability of ground state.Mysteries of High Temperature SuperconductorsBrittle, Creamic, Not shiny, Not metallic Magnetic inside, make your own. How they work is still a mystery.Magnetic Flux through Superconducting ring.Magnetic flux through superconducting ring cannot change. From Faraday's Law∮ 𝐸⋅𝑑 𝑙=− 𝑑Φ_{mag}𝑑𝑡 Assume: ∮ 𝐸⋅𝑑 𝑙≠0 Because 𝑅=0 in a superconductor, this would imply: 𝐼= emf𝑅→∞ and is impossible. Therefore 𝑑Φ_{mag}𝑑𝑡=0 must always be true for the flux through a superconducting ring. InductorFor a solenoid in steady state:𝐵=𝜇_{0}𝑁𝐼𝑑. Let the current change→Induces emf in every loop: emf_{loop}= = 𝑑𝑑𝑡 =
𝑑𝐼𝑑𝑡on each loop emf_{tot}=𝑁(emf_{loop})=
𝑑𝐼𝑑𝑡induced emf opposes the change InductanceLet inductance of solenoid 𝐿=
Because of Faraday's Law, coils of wire take awhile to reach steady state. emf_{tot}=𝐼*(resistance)=𝐿
𝐼=𝐼_{0}[1−𝑒^{−(resistance*𝑡/𝐿)}]=𝐼_{0}[1−𝑒^{−𝑡/𝜏}] where 𝜏=𝐿/(resistance) The higher the inductance, the longer it takes to reach steady state and long time constant→inductors are used to filter out highfrequency noise. Source and Referencehttps://www.youtube.com/watch?v=gKWy9FVvkHY&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=25©sideway ID: 200200202 Last Updated: 2/2/2020 Revision: 0 Latest Updated Links

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