Week 29

Physics:

  • Reading: Knight, Ch 38
  • Problems: Ch 38, probs 2, 3, 4, 5, 7, 12, 15, 21, 22, 24, 27, 31, 34, 38, 51, 64
    • Due as usual online 11:59 Friday eve.
  •  Notes:
    • #12: since fluorescence excitation (e.g. as used in cellular imaging in biology) depends on absorption of photons, it may take more (or less? You decide) power to excite fluorescent labeling molecules the same number of times when using different color lasers.
    • #27: Bohr atom problems like this always show up on the physics GRE, as are particle-in-a-box calculations (#51).
    • #31: note that you are showing that angular momentum is quantized! This is very important in the heat capacity of diatomic gasses (like air…)
  • Learning goals:
    • It is very important to know some of the basic formulae and how to use them, in particular:
      • The wavelength of light in terms of its energy
      • The wavelength of a material particle in terms of its momentum (de Broglie wavelength)
      • The basics of the Hydrogen energy spectrum (assuming I give you the ionization energy of 13.6Ev)
      • How to derive and use the particle-in-a-box energy levels. (This is related to how fluorescent molecules emit light, quantum dots absorb sunlight for photocells, etc. It is also a very common simplification in all advanced physics).

Circuits:

Reading:

  • Review op-amps circuits, especially integrators.
  • Questions:
  1. Your hard-drive circuit will have up-and-down voltage pulses with a period of about ~ 50ms. Design an op-amp integrator to integrate over this time period.
    1. You need feedback at DC; if you have 0.5V of DC offset coming into the integrator, what will your output DC voltage be, based on your resistor choices for your integrator circuit stage?
  2. You want to remove the DC offset (constant voltage offset) after your differential amplifier circuit stage and before the integrator stage. To do this you use a high-pass filter. Assuming your voltage signal looks like a square wave with period 40ms, what f3dB should you use? Design a circuit that will work for this, with a large safety margin.
  3. Transformers.
    1. You may assume that V2/V1 = N2/N1 for a transformer with turns ratio N2/N1, and that (since power P = I1 V1 = I2 V2 is conserved), I2/I1 = N1/N2.
    2. In class, you found that a community of 1e4 houses draws a total of 25kA of current at 120V. Using that information, what is the effective resistance of the community?
    3. Now assume we are using a transformer of turns ratio N2/N1 = 1/80 to step the voltage V1 DOWN to the voltage V2 = 120V at the houses. What are the voltage and current (V1 and I1) on the power line?
    4. Use Ohm’s Law to determine the “effective resistance” the community of houses looks like from the perspective of the power line. Write a formula for it in terms of the resistance you found for it at 120V and the turns ration of the transformers.

Calculus

  • FINAL EXAM Friday May 27, 1 pm in Sem 2 E3105
    • May use a personally prepared notesheet on an 8.5 inch x 11 inch piece of paper (both sides ok), a calculating device, and writing tools.
    • Blank copy of exam here.