EXAM 2 April 16, 1997 PHYS 208

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No notes, books, etc. may be used during this exam.

g = 9.8 m/sec^{2} |
Radius of the earth = 6.38 x 10^{6} m |
The mass of the electron is 9.11 x 10^{-31} kg. |

1 -------------- = 9.0 x 10 |
e = 1.60 x 10 ^{-19} C |

1. (10 points)

(a) What are the relationships among the formulae
for effective capacitance for series and parallel combinations
of capacitors and the effective resistance for series and parallel
combinations of resistors?

(b). What are the relations used in solving those DC circuits that cannot be solved solely by using series and parallel combinations of resistors? Justify the relations.

2. (30 points) Find the magnetic field inside a long solenoid which
has *n* turns/meter.

3. (30 points; from homework) For the circuit shown in the figure, find (a) the current in each resistor and (b) the power supplied by each EMF. After writing down equations whose solution will give all the currents, you may use the statement that the current in the resistor at the far right is 5V/(12R) downward.

4. (30 points) A capacitor is made of two concentric cylinders of
length L and radii R_{1} and R_{2}, with a dielectric
of constant kappa between the cylinders. If the inside cylinder
carries a charge +Q and the outside cylinder carries a charge -Q ,
determine the electric field in the dielectric, the potential
difference between the cylinders, and the capacitance of the device.
Neglect end effects.