EXAM 2 April 17, 1991 PS 208 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. 2 -19 g = 9.8 m/sec e = 1.6 x 10 C 9 2 2 1/(4 pi epsilon ) = 9.1 x 10 N m / C 0 -7 mu / (4 pi) = 10 T m/ A 0 -31 The mass of the electron is 9.11 x 10 kg. (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 two relations used in solving those DC circuits that cannot be solved solely by using series and parallel combinations of resistors? Justify these two relations. 2. (From homework) An electron enters a uniform magnetic -> -> field B at an angle theta to B . Determine the radius and pitch (distance between loops) of the electrons's helical path, assuming its velocity v is known. 3. Determine the current through each of the resistors in the figure below, where the resistance of each is the same . Show all the equations that would be necessary to solve the problem if the resistors were not all the same, and then use symmetries to simplify and solve the problem. --------R4-------------R2--------- | | | V R5 V The high side of the potentials | | | is on the geometrically lower -------R3-------------R1--------- side in both cases. 4. A parallel-plate capacitor of size a by b with the plates a distance d apart is filled with two dielectrics, each filling half of the capacitor. Show that the capacitance is given by epsilon a b kappa + kappa 0 1 2 C = -------------- --------------- d 2 where the kappa's are the relative permeabilities of the two dielectrics.