Sample questions for Test 3

1) Which device has higher resistance, a hair dryer or a night light?

2) Suppose you have a certain amount of a conducting substance, and you're going to make a resistor out of it.
  (a) What shape should you form to make a resistor with the lowest resistance? With the highest resistance?
  (b) If the stuff's resistivity is some value (rho), and you form it into a cone of height h and radius (at the fat end) of R, what is the resistance of this cone? Does it matter which end is up?

3) Given 4 resistors all of equal resistance R, you might connect them in various configurations. What different values of equivalent resistance can you get, and what is at least one configuration for each value? (Use all four resistors in every configuration.)

4) Suppose there's a wire lying along the y-axis and carrying a current of 2 A. Also suppose that there's a square loop of wire lying in the xy plane. The loop is 4 cm on a side and carries a current of 3 A; the loop is centered at the point x=5cm, y=0. What is the force on the loop?

5) Suppose a wire of radius R carries a total current I, and that the current density is proportional to the square root of the distance from the axis of the wire. What is the resulting magnetic field as a function of r, the distance from the wire's axis?

6) We charge up a 10 microfarad capacitor to 20 V, and then connect its two leads to the two leads of a 15 millihenry inductor. What is the maximum current that subsequently flows? How long does it take for the capacitor to discharge completely? (yes, assume that there is no resistance in the circuit.)

7) Suppose all of space is filled with current! This current flows in the +z direction, and has current density
J(r)=(J-sub-o)*exp(-(r/R)**2), where J-sub-o and R are constants.
  (a) How much current is this, altogether?
  (b) Suppose this same total amount of current were confined to a wire of radius R, and distributed uniformly throughout that wire. What would that uniform current density be?
  (c) Given the non-uniform current density, what is the magnetic field everywhere?

8) You've decided to go into the electricity-generation business. You've got a large, 0.05T magnet and a rotatable, rectangular frame, which is 30 cm by 50 cm. You're going to wind wire around the perimeter of this frame, maybe more than one time, and then you're going to rotate this frame in the magnet's field 60 times per second, so as to generate 60-Hz electrical power.
  (a) Is this the right frequency of rotation? Will this scheme generate an ac voltage between the two ends of your wire?
  (b) If this is a sound scheme, how many loops of wire will you need in order to generate a voltage whose peak-to-peak (from greatest positive voltage to most negative voltage) amplitude is 320 V?