NAME:___________________________

Laboratory section number (or day/time):___________________________

PHYS345 First Midterm Exam October 28, 1999

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.

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

Be careful with units, signs, and significant figures.

1. (20 points)

 Consider the following model of sound system, a stereo amplifier and speaker, designed to put 25 W into an 8 ohm speaker. What would be the source voltage needed to get 25 W at the speaker shown as RL? At that voltage, what would the power be if a 4 ohm speaker is connected instead? In the circuit at right, find the value of Is that will reduce the voltage across the 4 ohm resistor to zero. What if the 2 ohm and 6 ohm are interchanged? If a series RLC circuit is resonant at 60 Hz, does it become inductive or capacitive when the frequency is lowered to 50 Hz?

2. (20 points)

1. You and an engineering partner are struggling with a difficult signal acquisition problem. You are attempting to monitor the rotational stability of a small dc motor with a tachometer that produces a signal of 100 mV at 12,000 rpm (200 Hz). Unfortunately the measurement is plagued by a noise source of 10 mV at 60 Hz arising from pickup from a neighboring power transformer.

To start thinking about the problem, your partner calculates the ratio of the signal voltage to the noise voltage in dB. What value for the so-called signal-to-noise ratio should be reported to your boss?

2. Benefiting from your exposure to PHYS345, you attempt to lower the impact of the noise by constructing a simple RC high-pass filter with a cutoff frequency close to 200 Hz. However you only have available a 1.5 mF capacitor and several 1.0k resistors. Design and sketch the circuit required.

3. What new signal-to-noise ratio can be achieved by using this filter?

3. (20 points)

An electrical engineering firm has designed a motor for your sophomore design project. You specified that it should be 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 mF capacitor was added in parallel with the motor. Unfortunately the motor was actually wound with an inductance of 61 mH and a resistance of 30 ohm because of typographical errors in the FAX to the motor manufacturer.

1. What power is delivered by the voltage source?

2. What power is dissipated by the motor?

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

4.  (20 points)

 A young MacGyver enthusiast is attempting to design a simple switched RC circuit to use as a fuse timer. The child has a 5 F capacitor and one AAA cell with an emf of 1.5 V and an internal resistance of 0.6 ohm. If the fuse will ignite when the capacitor is charged to a voltage of 1.0 V, how much time does the youngster have to vacate the premises? With a never ending enthusiasm for adding batteries to a circuit, the youngster connects a fresh 9 V lithium battery as shown. Now how much time expires after switch closure until the fuse is ignited?

5.  (20 points)