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UVM PHYS 012 - Self Inductance, Transformers, and Circuits Containing Inductors
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PHYS 012 1st Edition Lecture 17 Outline of Last Lecture I. Problem: A conductive metal bar of mass m, making contact with an electric circuit with resistance R, is falling straight downward. Find an expression for the terminal velocity of the bar, assuming no air resistance, resistance within the circuit wires, andno friction between the bar and the wires.a. ΦB = ΣBΔAcosθb. As bar falls, Iind. is counter clockwise.c. Forces acting on bar: FB oriented upward, Fgrav. oriented downward.i. FB = ILBii. Fgrav. = mgd. ΣF = ILB – mg = ma; a = (ILB)/m – ge. εind. = -N (ΔΦB/Δt) = -BLvf. Iind. = |εind.|/R = (BLv)/Rg. a = {[(BLv)/R]LB}/m – g = {B2L2v}/Rm – gh. At terminal velocity, a = 0.i. {B2L2v}/Rm – g = 0ii. v = (gRm)/( B2L2)II. Self-Inductance *switch has just been closedThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. The increasing currents in the diagrams above when the switch is first closed will create a magnetic field and a change in flux. This will cause a back (opposing) εmfind.Outline of Current Lecture III. Self inductance constant, La. Measured in Henrys (H)i. 1 H = 1 (Vs)/Ab. Depends on configurationc. For solenoid: L = (N2Aμ0)/li. εind = -L(ΔI/Δt)ii. N (ΔΦ/Δt) = -L(ΔI/Δt) ; L = (NΦ)/Iiii. Φ = Aμ0(N/l)IIV. Energya. Depends on currentb. For solenoid, energy = (AlB2)/2μ0V. Energy density, μBa. μB = B2/2μ0i. True for energy density of any magnetic field in free space.VI. RL circuits: circuits with a resistor and an inductora. Back εmf is generated when I is increasing. No εmf is generated when I is constant.i. I = (ε/R)(1-e-t/τ)1. τ = time constant = L/Rii. When t = 0, I = 0.iii. As t approaches infinity, I approaches ε/R.b. Forward εmf is generated when I is decreasing.i. I = I0e-t/τii. When t = 0, I = I0. iii. As t approaches infinity, I approaches 0.VII. Transformersa. Magnetic field will constantly be switching directions, causing a constantly changing flux which generates a continuous εmf.i. Diagram above shows only one direction the magnetic field can be going.ii. The change in flux will be the same in both the primary and secondary circuits.iii. Ip/Is = Vs/Vp = Ns/NpVIII. LC Circuits: circuits containing an inductor and a capacitora. Capacitor is initially fully-charged, causing I to increase.b. Imax is reached when charge on capacitor is zero.i. Energy transformed from electric field to magnetic field.c. Current causes charge to build up on opposite capacitor plate, causing the polarity of the capacitor to reverse.d. This reversed polarity on the capacitor creates a current flowing in the opposite direction and increasing its magnitude to Imax.e. The current will continue switching directions around the circuit like this with an angular frequency (ω0) equal to 1/√(LC), assuming no resistance.f. Still charges create an electric field, moving charges create a magnetic field, and accelerating charges create


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UVM PHYS 012 - Self Inductance, Transformers, and Circuits Containing Inductors

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