Recitation section number (or day/time):___________________________

PHYS345 First Midterm Exam October 8, 1998

This is a closed book exam.

Programmable calculators and graphing calculators may be used during this exam.

Since this exam booklet may be separated for grading; it is important to:

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. (20 points)

Justify your answers in all cases!

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

  2. Two lamps A and B of identical resistance are connected in series to a battery having negligible internal resistance -- each lamp glows with the same intensity. Lamp A is suddenly shorted out by connecting a wire of negligible resistance across its terminals. Specify as completely as possible what happens to the intensity of each lamp.

  3. Consider the circuit shown with three identical resistors and an ideal current source. After the switch is closed, does the voltage across the current source increase or decrease? emf with three resistors

  4. Construct the Thevenin generator that would represent this circuit. current source and two resistors

2. (30 points)

Consider the following circuit that represents a small penlight, one alkaline AAA cell connected to a lamp. The AAA cell provides an emf of 1.5 V and has an internal resistance r1 of 0.6 ohms. The lamp resistance R may be assumed to be 7.0 ohms.

  1. What is the current through the lamp?

  2. What is the terminal voltage of the AAA cell?

[simple circuit]
In an attempt to increase the brightness of the lamp, an enthusiastic child finds a new 9 V lithium battery and adds it in parallel to the lamp and AAA cell as shown. A fresh lithium 9 V battery has an internal resistance r2 of about 18 ohms.

  1. What is the current through the lamp now?

  2. What is the terminal voltage of the AAA cell now?

  3. Was adding the 9 V battery worth it? (Consider power delivered and dissipated in each element.)
[multiloop circuit]

3. (30 points)

An electrical engineering major has designed and constructed a motor for your sophomore design project. It has been wound with an inductance of 16 mH and a resistance of 3.0 ohm. You had specified that it be optimized for the best possible power factor at 60 Hz; consequently, a 354 microFarad capacitor was added in parallel with the motor, as shown below.

Optimized motor circuit

  1. Operated at 120 V, what is the current through the motor when operated at 60 Hz?

  2. What power is delivered by the voltage source?

  3. What power is dissipated by the motor?

Your complete project was so innovative that your engineering professor entered it in an international competition. You arrive in Germany for the competition before remembering that the line frequency there is 50 Hz.

  1. What is the power factor of this circuit at 50 Hz?

  2. What capacitance do you need to correct the power factor back to unity?

4.  (30 points)

Your friend is having trouble starting an old car. Eager to apply your new expertise with circuits, you decide to determine the internal resistance of the battery to see if a new 12 V battery is needed. You phone your physics instructor, widely known for his generosity, and borrow a digital multimeter. You also borrow a 10 ohm resistor since you recall that the battery must be loaded to measure the effects of internal resistance, observed by connecting the resistor to the battery and measuring the change in the battery's terminal voltage.

  1. What power should the resistor be able to dissipate adequately to conduct this test successfully?

Arriving back at the car, you discover that unfortunately the voltmeter mode of the DMM has been damaged. However the ammeter mode still seems to be working so you rig the circuit shown.

  1. A current of 1.10 A is measured with the DMM. What is the internal resistance of the battery?

  1. While conducting this test, your friend attempts to start the car again. When the ignition switch is closed, the DMM measures a current of 0.12 A. What is the resistance of the starter motor?

Last updated Oct. 8, 1998.
Copyright George Watson, Univ. of Delaware, 1998.