UNIVERSITY OF MASSACHUSETTS DARTMOUTH

COLLEGE OF ENGINEERING

EGR 101 INTRODUCTION TO ENGINEERING I

Ø  This assignment is due Thursday, October 23, 2013.

Ø  Use engineering paper.

Ø  Show all of your steps.

Ø  Present your work neatly and clearly.

Ø  Box your final answers.

Problem 1

Consider the following circuit that consists of series and parallel capacitors. Each capacitor has capacitance equal to .

Ø  Find the total capacitance in . Let C represent a 0.047 µF capacitor.

Total Capacitance is 2C in series with C.

Problem 2

Consider the following circuit in which and each capacitor has capacitance equal to 12 pF.

Let C represent a 12 pF capacitor.

Ø  Draw a simple circuit with one total resistor and one total capacitor, and label their values with proper units.

Ø  Find the time constant in ms.

Problem 3

Consider a capacitor with a plate area equal to . The plate spacing is 0.01 mm.

The design requires a capacitance of 923.9 nF. In order to select the dielectric material, calculate the following:

Ø  The material permittivity in F/m, and

Ø  The material relative permittivity .

Ø  What material do you select from Table 12.1 on p. 368 based on your relative permittivity?

Ø  By what factor should you increase or decrease the capacitor spacing if the capacitor is 923.9 pF instead of 923.9 nF?

From Table 12.1 on page 368 of the text, Tantalum Oxide has a relative permittivity of 11.6.

The spacing between the plates needs to be increased from 0.01 mm to 10 mm. This is 1000 times the separation distance in the original capacitor. This makes sense, since the capacitance changed by a factor of 1000.

Problem 4

Consider the following circuit in which the SPDT switch is set to discharge the capacitor and has been closed for a long time. The capacitor is and .

Ø  Use Ohm’s law to find in order to limit the initial discharge current to 5 mA.

Ø  Report in ms the time constant of the circuit in the discharge mode.

Ø 

In the discharge mode, the voltage across the capacitor is given by

where .

Ø  Find an expression for the current as a function of time, .

Ø  Plot in the interval using Excel with a time interval equal to and fill in the first 25 rows.

  1. Submit a copy of the graph.
  2. Submit a print of the table that consists of two columns: the left column containing time and the right column containing current values.

t / i(t)
sec / Amperes
0 / -0.005
0.005 / -0.003894004
0.01 / -0.003032653
0.015 / -0.002361833
0.02 / -0.001839397
0.025 / -0.001432524
0.03 / -0.001115651
0.035 / -0.00086887
0.04 / -0.000676676
0.045 / -0.000526996
0.05 / -0.000410425
0.055 / -0.000319639
0.06 / -0.000248935
0.065 / -0.000193871
0.07 / -0.000150987
0.075 / -0.000117589
0.08 / -9.15782E-05
0.085 / -7.13212E-05
0.09 / -5.5545E-05
0.095 / -4.32585E-05
0.1 / -3.36897E-05
0.105 / -2.62376E-05
0.11 / -2.04339E-05
0.115 / -1.59139E-05
0.12 / -1.23938E-05
0.125 / -9.65227E-06
0.13 / -7.5172E-06