Fundamentals of Engineering Exam Review Electromagnetic Physics
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1 Dr. Gregory J. Mazzaro Spring 2018 Fundamentals of Engineering Exam Review Electromagnetic Physics (currently 5-7% of FE exam) THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409
2 FE Exam Subjects 2
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 = x C 1 proton holds a charge of q = x 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) 3
4 Electric Field & Coulomb s Law a field is a vector (with magnitude & direction) defined at all points in space, (x, y, z) Q 2 r a r12 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 Q 1 E field vectors D flux lines 4
5 Example: Electric Field (A) mn, away from the 2-nC charges (B) mn, away from the 2-nC charges (C) mn, towards the 2-nC charges (D) mn, towards the 2-nC charges The correct answer is (A). 5
6 Example: Electric Field & Potential V F QE Q The correct answer is (B). d 6
7 Gauss Law -- 1 of Maxwell s Equations which governs the behavior of electric fields Q encl = 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 7
8 Example: Gauss Law 8
9 Example: Gauss Law 9
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) L Also, real materials become more current-resistant as they heat up. 10
11 Example: Resistivity The correct answer is (C). 11 R r 2 P I R L A I J I J A A P 2 R 2 r I J A L L A J A r W
12 Capacitance & Stored Energy 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. 12
13 Example: Capacitance 13
14 Example: Electrostatic Energy 2 Qd 2 Q V E e A e A
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 15
16 Example: Electromagnetic Work 16
17 Magnetic Fields 17
18 Inductance & Stored Energy 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. 18
19 Example: Magnetostatic Energy 19
20 Example: Magnetostatic Energy 20
21 Lenz s Law / Induced Voltage induced electro-motive force (EMF), v emf (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 ) Iind (v induced) v emf I ind Lenz s Law ( B ind and I ind, for V emf ) -- the current induced in the loop generates a magnetic field to oppose the change in magnetic flux (B applied) 21
22 Example: Lenz s Law / Induced Voltage 22
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 righthand-rule, and whose magnitudes are related by the characteristic impedance of free space, h : E H h 377 W S E H 23
24 Example: Free-Space EM Waves (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 S E H E is parallel to the antenna H is perpendicular to the antenna E H 3 10 V cm 377 W H 2.6 μa cm 377 W The correct answer is (C). 24
25 Dr. Gregory J. Mazzaro Spring 2018 Fundamentals of Engineering Exam Review Selected Advanced Circuit-Theory Concepts THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409
26 Example: RC Circuit C v t V e 0 t/ RC v 10RC V e C almost completely discharged all energy stored in C = 10 mf was dissipated by R = 25 W W CV J The correct answer is (B).
27 Example: RL Circuit V Rt / L il t 1e R 10 V t 2 1 t il t e e A 5 W The correct answer is (D). 27
28 Example: Thevenin Equivalent 28
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. 29
30 Example: Power, AC Circuit P I V I R 4W 2 rms rms rms I 4 W A W rms The correct answer is (B). 30
31 Example: Op Amp v a v a v i2 i1 0 b v b v v v v R R o a 1 a v v o v v o b 0 v R R a v The correct answer is (C). 31
32 Example: Op Amp v a v a v i2 i1 0 b v b R 4 vb v2 v2 v2 R3 R v v 0 v R R vo 1va 1 v2 R o a a R v v o The correct answer is (C). 32
33 Gain / Decibels Gain (A) refers to the ratio of output-to-input voltage, current, or power. A v V V out in differential gain = A A v,diff p V P in,1 out P in Vout V in,2 V in A v,1 A v,2 V out V A A A out v v,1 v,2 Vin A A A db db db v v,1 v,2 Decibels are a convenient mathematical form used to express very high/low gain (up/down to very high/low values of V, I, P). 33
34 Example: Op Amp, Decibels A A 20log db v,diff 10 V in,1 V 40 V V db v,diff 10 Vout V in,2 20log db The correct answer is (A). 34 A A A A db db db db p p,1 p,2 p, db
35 Transfer Function Many calculations on linear circuits, assuming the circuit has reached sinusoidal steady-state, are easier to perform in the frequency (j) domain: Y j H j X j y t h t x t by the Fourier Transform, where h is the impulse response of the circuit and H is the transfer function of the circuit 10sin t 30 V L S v v H j j kω j kω 1 kω 35 input (x) = voltage, output (y) = voltage, system (h) = voltage divider
36 Example: Transfer Function 36
37 Example: Transfer Function v 1 Vo v1 Vin v1 0 v1 v MΩ 1 jc 5 MΩ v 2 V o in 20 MΩ 1 5MΩ jc j j V V o 20j 2.7 j jc V in The correct answer is (B). 37
38 Dr. Gregory J. Mazzaro Spring 2018 Grimsley Hall, Room THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409
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