When two electrical resistors with resistance r1 > 0 and r2 > 0 are wired in parallel in a circuit, the combined resistance r, measured in ohms (ω), is given by 1 r = 1 r1 + 1 r2 (a) find ∂r ∂r1 and ∂r ∂r2 after solving for r (e. g., r = . (b) describe how an increase in r1 with r2 held constant affects r. (will r increase or decrease? ) (c) describe how a decrease in r2 with r1 held constant affects r. (will r increase or decrease? )

Some material consisting of a collection of microscopic objects is kept at a high temperature. a photon detector capable of detecting photon energies from infrared through ultraviolet observes photons emitted with energies of 0.3 ev, 0.5 ev, 0.8 ev, 2.0ev, 2.5ev, and 2.8ev. these are the only photon energies observed. (a) draw and label a possible energy-level diagram for one of the microscopic objects, which has four bound states. on the diagram, indicate the transitions corresponding to the emitted photons. explain briefly. (b) would a spring–mass model be a good model for these microscopic objects? why or why not? (c) the material is now cooled down to a very low temperature, and the photon detector stops detecting photon emissions. next, a beam of light with a continuous range of energies from infrared through ultraviolet shines on the material, and the photon detector observes the beam of light after it passes through the material. what photon energies in this beam of light are observed to be significantly reduced in intensity (“dark absorption lines”)? explain briefly.

Gather reliable information to brent make his decision. to gather this information, use newspapers, call insurance companies or look at their web sites, and review consumer magazines and web sites. also, look at the manufacturer web site or for information about gas mileage. list the sources you use and take notes.

The atoms in a nickel crystal vibrate as harmonic oscillators with an angular frequency of 2.3 × 1013 rad/s. the mass of a nickel atom is 9.75 × 10-26 kg. what is the difference in energy between adjacent vibrational energy levels of nickel? (h = 6.626 × 10-34 j • s, , 1 ev = 1.60 × 10-19 j)