NAME:___________________________
Recitation section number (or day/time):___________________________
This is a closed book exam; the formula sheet provided is the only supplemental material permitted on this exam.
Programmable calculators and graphing calculators may be used during this exam, but not for storage of additional notes or formulas.
Show ALL work on problem sheet and only on that sheet.
Please read questions carefully.
Credit may be lost inadvertently if solutions are not neat and orderly.
Be careful with units, signs, and significant figures.
1. (12 points)
An enterprising PHYS208 student assembles the circuit shown in an attempt to determine the internal resistance of an old lithium 9 V battery. The student has connected a load resistance R of unknown value; the color coding of the resistor has been obliterated with time. Unfortunately the digital multimeters have been locked away for the semester; however, the student is able to scrounge up a cheap ammeter (resistance 1 ohm) and a cheap voltmeter (resistance 1000 ohm) for the test. 
The final circuit assembled by the student looks like this.
The reading on the voltmeter is 7.0 V and the reading on the ammeter is 77 mA.

As the most recent graduate of PHYS208 in your family,
you are called on to fix the family toaster.
Lately it has been burning the toast and they would like a demonstration of your
newfound abilities in manipulating electric circuits.
Stalling, you turn over the toaster and find the following information:
Rated 1500 W at 120 Vrms, 60 Hz.
Remembering that the power delivered to the load by an ac emf may be lowered via the
power factor, you grab a hefty capacitor (100 microfarad)
left over from your Punkin' Chunkin' project work and build the circuit shown:
What is the power now delivered to the toaster?
Using the circuit parameters from the preceding page,
consider the alternative circuit where the capacitor is added in parallel
to the toaster.
[Note: the formula for the impedance of a series RLC circuit may not be applied here!]
Another type of transmission line often encountered today is the flat cable, consisting of numerous parallel wires; these are commonly used to connect disk drives to computer boards for example. A typical configuration is 26 gauge wire (radius 0.20 mm) separated by 0.050 inches (1.27 mm).
a. Use Gauss's law to determine the electric field at a point between the two conducting shells when oppositely charged. Be sure to show the gaussian surface used and indicate the direction of the resulting field.
b. Use the resulting electric field to find the energy density u_{E} in the region between the conductors and then the total energy U stored by the capacitor.
c. Express the capacitance in terms of the parameters of the capacitor shown, by using U = Q^{2}/2C.
d. Evaluate the capacitance if a = 10 mm, b = 11 mm, c = 12 mm, and d = 13 mm.
e. A simple check of your true understanding of conductors and Gauss's law:
If identical charges are deposited on both conductors, say +1 microcoulombs, how are the charges distributed among the four surfaces?