Fundamentals of Engineering Exam Review …ece.citadel.edu/mazzaro/seminars/FE_Review_2018_Mazzaro.pdf · THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street,

THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA

171 Moultrie Street, Charleston, SC 29409

Dr. Gregory J. Mazzaro

Spring 2018

Fundamentals of Engineering

Exam Review

Electromagnetic Physics

(currently 5-7% of FE exam)

2

FE Exam – Subjects

3

Charge vs. Current

• charge is the basic unity of electricity (a property of protons & electrons)

particles that attract each other (opposite “charge”)

or repel each other (same “charge”)

• as EEs, we focus on the behavior of electrons

• fundamental unit of charge (SI system) = coulomb

1 electron holds a charge of

q = –1.602 x 10-19 C

1 proton holds a charge of

q = +1.602 x 10-19 C

• current = the flow of charge

• unit of current = ampere

1 ampere = 1 C / s (1 coulomb flowing past a point per second,

usually within a wire)

4

Electric Field & Coulomb’s Law

• a field is a vector (with magnitude & direction)

defined at all points in space, (x, y, z)

• an electric field (E) is the force that a unit charge

experiences (N/C) due to the presence of other

charges nearby governed by Coulomb’s Law

1Q

r

Q2

E

ar12

field vectors

flux lines

D

5

Example: Electric Field

(A) 0.431 mN, away from the 2-nC charges

(B) 0.719 mN, away from the 2-nC charges

(C) 0.431 mN, towards the 2-nC charges

(D) 0.719 mN, towards the 2-nC charges

The correct answer is (A).

6

Example: Electric Field & Potential

VF QE Q

d The correct answer is (B).

7

Gauss’ Law

-- 1 of Maxwell’s Equations which governs

the behavior of electric fields Qencl = charge contained in a

“Gaussian” surface

E = electric field intensity

dS is normal to the surface

and directed outward

(sphere)

an alternative to Coulomb’s Law for determining electric field, under symmetry

8

Example: Gauss’ Law

9

Example: Gauss’ Law

10

Resistivity

All real wires have a non-zero resistance.

• when current flows along a non-zero resistance,

voltage drops and energy is dissipated (as heat)

r = resistivity,

a material property (W-m)

Also, real materials become more

current-resistant as they heat up.

L

11

Example: Resistivity

2

22

22 2100 .05 0.1 7.85 W

RP I R

L A

IJ I J A

A

P RI J A

L L A

J A

r

r

r

The correct answer is (C).

12

Capacitance & Stored Energy

12

A capacitor is a linear circuit element which stores energy

in the electric field in the space between two conducting bodies

occupied by a material with permittivity e .

13

Example: Capacitance

13

1414

Example: Electrostatic Energy

22

2 2

0 0

Qd QV E

A Ae e

15

Voltage / Potential / Work

• energy must be expended to move charge

• work required to move charge through an

element or through a field, per charge = voltage

• unit of voltage = volt = 1 J/C

• can exist even when no current

is flowing “potential”

Circuit theory

Electromagnetic

theory

QV

16

Example: Electromagnetic Work

17

Magnetic Fields

18

Inductance & Stored Energy

18

An inductor is a linear circuit element which stores energy

in the magnetic field in the space between current-carrying wires

occupied by a material with permeability m .

19

Example: Magnetostatic Energy

20

Example: Magnetostatic Energy

21

induced electro-motive force (EMF), vemf (in volts)

-- potential difference generated in a loop by

applying a time-varying magnetic field B to the loop (“transformer EMF”)

and/or changing the area seen by the B field over time (“motional EMF”)

(B applied)

(v induced) indI

indI

emfv

Lenz’s Law ( Bind and Iind , for Vemf )

-- the current induced in the loop generates a magnetic

field to oppose the change in magnetic flux

Lenz’s Law / Induced Voltage

22

Example: Lenz’s Law / Induced Voltage

23

Free-Space EM Waves

Far away from a radiating antenna, the traveling fields

may be approximated as a plane wave, with E and H in

phase, whose vector directions are related by the right-

hand-rule, and whose magnitudes are related by the

characteristic impedance of free space, h :

377E

Hh W

S E H

24

Example: Free-Space EM Waves

S E H

310 V cm377 2.6 μA cm

377

EH

H

W W

E is parallel to the antenna

H is perpendicular to the antenna

(A) 2.6 mA/cm, parallel to the antenna

(B) 3.8 mA/cm, parallel to the antenna

(C) 2.6 mA/cm, perpendicular to the antenna

(D) 3.8 mA/cm, perpendicular to the antenna

The correct answer is (C).

THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA

171 Moultrie Street, Charleston, SC 29409

Dr. Gregory J. Mazzaro

Spring 2018

Fundamentals of Engineering

Exam Review

Selected Advanced

Circuit-Theory Concepts

26

Example: RC Circuit

26

/

0

10

010

0

t RC

C

C

v t V e

v RC V e

almost completely discharged

all energy stored in C = 10 mF

was dissipated by R = 25 W

22 61 1

10 10 150 0.11J2 2

W CV

The correct answer is (B).

27

Example: RL Circuit

27

/

2.5 2.5

1

10 V1 2 1 A

5

Rt L

L

t t

L

Vi t e

R

i t e e

W

The correct answer is (D).

28

Example: Thevenin Equivalent

29

RMS or Effective Value

Root-mean-squared (or effective)

values are an alternative

representation of the magnitude of

time-varying and periodic signals.

They allow us to calculate equivalent

V/I/P for AC circuits as if the V/I/P

quantities were DC values.

30

Example: Power, AC Circuit

2

4

2

1

2

4

14.4 A 4

829 W

rms rms rms

rms

P I V I R

I

W

W

The correct answer is (B).

31

Example: Op Amp

a bv v 2 1 0i i va

vb

1

2 1

21

1

1

0

0

20040

5

o a a

b a

o

o

v v v v

R R

v v

Rv v

R

v

v

The correct answer is (C).

32

a bv v 2 1 0i i va

vb

42 2 2

3 4

2 1

22

1

2

200 40

205 41

00

200 401 1

5 41

4041 40

41

b

o a a

o a

o

Rv v v v

R R

v v v

R R

Rv v v

R

v

v

The correct answer is (C).

Example: Op Amp

33

Gain / Decibels

Gain (A) refers to the ratio of output-to-input

voltage, current, or power.

out outv

in in

p

V PA A

V P

“differential” gain = outv,diff

in,1 in,2

VA

V V

Av,1 Av,2VoutVin

outv v,1 v,2

in

VA A A

V

dB dB dB

v v,1 v,2A A A

Decibels are a convenient mathematical form

used to express very high/low gain

(up/down to very high/low values of V, I, P).

34

Example: Op Amp, Decibels

dB outv,diff 10

in,1 in,2

20logV

AV V

0 1 2

dB

v,diff 10

40

20log 40 32 dB

V V V

A

The correct answer is (A).

dB dB dB dB

p p,1 p,2 p,3

100 25 9 134 dB

A A A A

35

Transfer Function

y t h t x t

Y j H j X j

Many calculations on linear circuits,

assuming the circuit has reached

sinusoidal steady-state, are easier to

perform in the frequency (j) domain:

by the Fourier Transform, where h is the impulse response of the circuit

and H is the transfer function of the circuit

10sin 30 Vt

L

0.1 || 3 kΩ1030

0.1 || 3 kΩ 1kΩ2

Sv v H j

j

j

input (x) = voltage, output (y) = voltage,

system (h) = voltage divider

36

Example: Transfer Function

37

Example: Transfer Function

1 in 11 20 0

20 MΩ ||1 5MΩ

oV v V vv v

j C

v1

v2

in

6 6

in

20 MΩ ||1

5 MΩ

1 2 60 .001 10 2.7 10

20 2.71

5 20 2.7

0.53 82

o

o

j CV V

j C j j

jV

V j

The correct answer is (B).

THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA

171 Moultrie Street, Charleston, SC 29409

Dr. Gregory J. Mazzaro

Spring 2018

[email protected]

Grimsley Hall, Room 312

843-953-0429

http://ece.citadel.edu/mazzaro