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  1. Practice problem

    Count the active energy modes →

    Intermediate · Apply a principle. Find its internal energy in the classical translational model.

  2. Practice problem

    Count the maxima that survive the slit envelope →

    Advanced · Connect concepts. How many principal maxima, including the central one and both sides, survive the ideal single-slit envelope?

  3. Practice problem

    Count the three directional changes →

    Advanced · Connect concepts. What is its first-order fractional volume increase?

  4. Practice problem

    Covering the grating changes sharpness →

    Intermediate · Compare cases. What is the new Rayleigh estimate of the minimum resolvable wavelength separation?

  5. Practice problem

    Cross the river, then measure the drift. →

    Intermediate · Connect concepts. How far downstream does the swimmer land?

  6. Practice problem

    Crossing without being swept downstream →

    Intermediate · Connect concepts. Find the crossing time.

  7. Practice problem

    Design for an angular separation before choosing magnification →

    Intermediate · Find a missing quantity. What minimum aperture diameter meets the ideal Rayleigh criterion?

  8. Practice problem / FREE SAMPLE

    Differentiate potential with its sign →

    Intermediate · Read graphs & measurements. Translate a position-dependent potential into a local field.

  9. Practice problem

    Distance after a direction change →

    Advanced · Connect concepts. Find the total distance travelled.

  10. Practice problem

    Do the electric fields cancel at the midpoint? →

    Beginner · Connect concepts. What is the electric field at the midpoint?

  11. Practice problem

    Does a faster particle take longer to complete a circle? →

    Intermediate · Compare cases. What is the ratio of the second orbital period to the first?

  12. Practice problem / FREE SAMPLE

    Does a longer smooth track mean a slower finish? →

    Intermediate · Apply a principle. Gravity remembers the change in height, not the length of the path.

  13. Practice problem

    Does friction always equal μN? →

    Beginner · Compare cases. What friction force acts on the case?

  14. Practice problem

    Does the shortcut meet the tolerance? →

    Advanced · Compare cases. By what percentage does this underestimate the exact inferred G, relative to that exact G?

  15. Practice problem

    Doping does not remove the minority carriers →

    Advanced · Connect concepts. What is its equilibrium hole density p?

  16. Practice problem

    Doubling voltage changes heating →

    Intermediate · Compare cases. Find its new power dissipation.

  17. Practice problem

    Eight drops become one →

    Intermediate · Compare cases. Find the radius of the final spherical drop.

  18. Practice problem

    Emission is not net cooling →

    Intermediate · Connect concepts. Find its net radiative power loss.

  19. Practice problem

    Energy carried by the magnetic field →

    Intermediate · Apply a principle. Find its stored magnetic energy.

  20. Practice problem

    Energy gained by a negative probe →

    Intermediate · Apply a principle. What is its final kinetic energy?