IB Physics Capacitance

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A tutorial sheet on capacitance, a section in HL topic 11, is given below.

  1. What is the meaning of the term capacitance?
  2. For a given capacitor at a constant temperature, is the "capacitance" constant?
  3. Write down an expression for the capacitance of a charged sphere of radius R in a vacuum.
  4. Express the unit of capacitance in terms of SI base units.
  5. An uncharged capacitor of capacitance C is connected in series with an open switch across a 12 V DC battery of zero internal resistance and a resistance R. The switch is now closed. Describe the build up of charge on the capacitor.
  6. A capacitor of value C has a charge Q. It is connected in series to a resistor R and an open switch. The switch is now closed. Describe the current through the resistor.
  7. Two capacitances C1 and C2 are connected in series across a battery. Find an expression for the total capacitance. Show your working.

  8. Two capacitances C1 and C2 are connected in parallel across a battery. Find an expression for the total capacitance. Show your working.

  9. An uncharged capacitor is charged by being connected by wires to a battery of constant emf and zero internal resistance. (a) Is the current in the connecting wires equal to the rate of increase of charge on the plates? (b) Is there a current in the space between the plates? (c) Is there a magnetic field in the space between the plates? (d) Is the work done by the battery equal to the energy stored in the capacitor?

  10. In the IB Physics Data Booklet a formula is given for the capacitance of a parallel plate capacitor. What are the assumptions for this formula?
  11. To take into account the finite area of the plates of a capacitor see the Berkeley Physics Course Volume 2 Electricity and Magnetism by E M Purcell (red version page 97, blue version page 105) for a table of end correction values. Another reference is Physics Education, Vol 17, Number 2, March 1982, page 35.

HSC Physics Bouncing Superballs

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A tutorial sheet involving collisions is given below.

  1. A tennis ball is dropped from a height h1. It bounces to a height h2. Is momentum conserved in the collision? Is kinetic energy conserved in the collision? Is energy conserved in the collision?
  2. A steel ball bearing of mass M moving at a speed U collides in a line with two balls of mass M that are at rest. Why doesn't each ball move at U/3 after the collision?
  3. Imagine two superballs, of different mass, placed one on top of the other and dropped from a height H very large compared to the radius of each ball. Assuming an elastic collision with the ground, what is the maximum height to which the top superball can bounce? [9 H]
  4. For more multi-highball problems see Anthony Anderson, Physics Education, vol 34, number 2, March 1999, page 76.