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EXAM 2                         April 16, 1997                         PHYS 208
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If you need a constant not given here or do not understand a problem, please ask me about it.
No notes, books, etc. may be used during this exam.

 g = 9.8 m/sec2 Radius of the earth = 6.38 x 106 m The mass of the electron is 9.11 x 10-31 kg. ``` 1 -------------- = 9.0 x 109 N m2/C2 4 pi epsilon0 ``` e = 1.60 x 10-19 C
For all problems, place the equations representing the physics principles you are using in the box on the page. You may use the general form of the equation or the form you get applying the principle to the problem at hand. If no diagram is applicable to a problem, write "none" in the diagram section.

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 R1 and R2, 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.