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### PHYS208 Final Exam       December 16, 1997

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.

Credit may be lost inadvertently if solutions are not neat and orderly.

Be careful with units, signs, and significant figures.

1. (12 points)

1. An induced current appears in the direction shown when the straight movable wire segment is moved to the left. Is the direction of the uniform magnetic field that is present into or out of the page? Briefly justify answer.

2. An electron moves horizontally to the East through a magnetic field that is directed downward. Which direction is the magnetic force on the electron?

3. For what value of the power factor is the impedance purely resistive? Purely inductive?

4. What is the electric field halfway to the center of a conducting sphere charged to a potential of 15 V? What is the potential halfway to the center?

5. The driving angular frequency applied to a certain RLC series circuit is less than the circuit's resonant frequency. Does the current lead or lag the emf?

6. Does the torque that a current loop experiences when placed in a magnetic field tend to rotate the loop in a direction such that the magnetic flux increases or decreases?

2. (15 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. What is the value of the internal resistance? What is the value of the load resistance? The ratio of voltage measured across the load to the current measured through the load is 90.9 ohm. Why is the actual value of the load resistance different from this "measured" value?

3. (15 points)

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?

4. (8 points)
A learning opportunity to test your true understanding of phasors...

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!]

1. What is the rms current through the toaster?

2. What is the rms current through the capacitor?

3. What is the rms current through the emf?

4. Sketch a phasor diagram showing the three current phasors relative to the voltage phasor. Does the emf see a capacitive or inductive circuit connected to it?

5. (25 points)

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).

1. Model the inductance per unit length of this cable by calculating the flux linkage between neighboring wires.

2. Evaluate the inductance per meter of this flat cable for a pair of wires.

3. As a homework exercise you derived the capacitance per unit length for this geometry; the result was  / ln[(d-a)/a]. Assuming a dielectric constant of 3.2, evaluate the capacitance per meter of this flat cable.

4. What fraction of the speed of light is the phase speed for the flat cable on the preceding page?

5. How long does it take for a signal to travel from a disk drive to a computer board using a standard 18 inch flat cable?

6. (25 points)

The spherical capacitor is often considered because it is finite-sized but without the complication of a fringing field, present for the parallel-plate capacitor usually considered. Find an expression for its capacitance using ENERGY CONSIDERATIONS.

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 uE 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 = Q2/2C.

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?

• #1, inner surface
• #1, outer surface
• #2, inner surface
• #2, outer surface

"http://www.physics.udel.edu/~watson/phys208/exams/fin-97f.html"
Last updated Dec. 22, 1997.
Copyright George Watson, Univ. of Delaware, 1997.