Recitation section number (or day/time):___________________________

PHYS345 Final Exam          December 17, 1998

This is a closed book exam. One 3"x5" note card is permitted; this card should be turned in with your exam papers.

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.  Motors and dimming lights (20 points)

Use what you have learned about ac circuits this term to understand some of the issues involving power distribution to industrial motors. Quoting from the textbook:

Large motor starting currents drawn through transformer and line impedances drop the voltage at the motor and therefore for other loads fed from that line. A sufficiently low-impedance transformer and line must be provided to keep the load voltages within established tolerances.

In the following circuit schematic assume that the transformer reactance is 0.15 ohm and the line reactance is 0.10 ohm.

Distribution lines for industrial motor service

  1. What is the voltage at the distribution point A (voltage supplied to the motor) if the full load current is 150 A with a power factor of 90% (starter bypassed with switch closed)?

  2. What is the voltage at point A if the current with the starting coil engaged (switch open) is 2.5 times the running current in part a, with a power factor of 50%?

  3. Why do lighting circuits connected to the distribution point dim when the motor is started?

2.  Digital Comparator (15 points)

  1. Design a combination of two-input logic gates that will have a single output C that is true if input A is larger than input B, according to the following truth table.

     A   B   C 
    0 0 0
    0 1 0
    1 0 1
    1 1 0

  2. Design another combination of two-input logic gates that will have a single output C that is true if a two-bit input A is larger than a two-bit input B. There will be four inputs: AH, AL, BH, and BL.

3.  Too many batteries! (20 points)

A 9.0 V lithium battery (internal resistance 18 ohm) has been connected to a real inductor (inductance of 1.0 H and resistance of 27 ohm) as shown.

  1. What is the current in the inductor a long time after the circuit has been formed?

  2. What is the power delivered by the battery to the rest of the circuit?

Real inductor connected to real battery
A 1.5 V AA cell (internal resistance 0.6 ohm) is added in parallel to the 9.0 V battery and inductor as shown.
  1. What is the current in the inductor a long time after this circuit has been formed?

  2. How long does it take for the inductor to change to its new current value? (Use five time constants.)
Real inductor connected to two real batteries

4.  Gray counter (15 points)

Determine the state diagram for this two-bit counter. D FF 2-bit Gray counter
How would you reconfigure the counter to reverse the sequence determined above? (Show all work!) reversed D FF 2-bit Gray counter

5.  Real-world differentiator (20 points)

The following differentiator circuit has been designed for a signal conditioning application. The resistor has a value of 100k and the capacitor has a value of 1.0 microfarad.

  1. At what frequency is the magnitude of the gain 40dB?

  2. What input impedance does the signal see at this frequency?

inverting differentiator
  1. The designer deems the input impedance in the above circuit to be too low and a non-inverting configuration is tried. What are the limitations to the desired differentiator response? That is, over what range of frequencies will it differentiate accurately? (Hint: consider the Bode plot.)
non-inverting differentiator
  1. Unfortunately it is discovered that an instability results unless an additional resistor Rs of 100 ohm is added as shown. Now what is the range of frequencies for accurate differentiation?

  2. At frequencies high enough that XC may be ignored compared to Rs, what is the gain in dB?
stabilized non-inverting differentiator

6.  The 555 Timer (15 points)

The 555 integrated circuit is an extremely useful package of analog and digital electronics for building timing circuits. In the circuit shown, the 555 is being used to create a digital clock signal. astable 555 configuration
The following text has been lifted from the manufacturer's literature:
  astable operation

As shown in Figure 12, adding a second resistor RB to the circuit of Figure 9 and connecting the trigger input to the threshold input causes the timer to self-trigger and run as a multivibrator. The capacitor C will charge through RA and RB and then discharge through RB only. The duty cycle may be controlled, therefore, by the values of RA and RB.

This astable connection results in capacitor C charging and discharging between the threshold-voltage level (0.67 VCC) and the trigger-voltage level (0.33 VCC). As in the monostable circuit, charge and discharge times (and therefore the frequency and duty cycle) are independent of the supply voltage.


That is, the charging time tH is the time it takes to charge the capacitor from 5 V to 10 V when connected to 15 V through the resistance RA + RB. (VCC = 15 V has been assumed.) The discharging time tL is the time it takes to discharge the capacitor from 10 V to 5 V when connected to ground through the resistance RB.

From the information given above, determine a formula for the frequency of the clock. Check its validity against the timing diagram shown below.

  astable 555 timing diagram

Last updated Dec. 17, 1998.
Copyright George Watson, Univ. of Delaware, 1998.