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
FE Exam Subjects 2
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) 3
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
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). 5
Example: Electric Field & Potential V F QE Q The correct answer is (B). d 6
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
Example: Gauss Law 8
Example: Gauss Law 9
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
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 2 2 2 J A r 100.05 0.1 7.85 W
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
Example: Capacitance 13
Example: Electrostatic Energy 2 Qd 2 Q V E e A e A 2 2 0 0 14
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
Example: Electromagnetic Work 16
Magnetic Fields 17
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
Example: Magnetostatic Energy 19
Example: Magnetostatic Energy 20
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
Example: Lenz s Law / Induced Voltage 22
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
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
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
Example: RC Circuit C v t V e 0 t/ RC v 10RC V e C 0 0 10 almost completely discharged all energy stored in C = 10 mf was dissipated by R = 25 W W 1 2 1 10 10 6 CV 150 0.11J 2 2 2 26 The correct answer is (B).
Example: RL Circuit V Rt / L il t 1e R 10 V 2.5 2.5 1 t 2 1 t il t e e A 5 W The correct answer is (D). 27
Example: Thevenin Equivalent 28
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
Example: Power, AC Circuit P I V I R 4W 2 rms rms rms I 4 W 2 1 2 14.4 A 4 829 W rms The correct answer is (B). 30
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 1 2 1 v v o b 0 v R R 200 5 2 1 a v 1 0 40 The correct answer is (C). 31
Example: Op Amp v a v a v i2 i1 0 b v b R 4 vb v2 v2 v2 R3 R4 205 41 v v 0 v R R 2 1 2 vo 1va 1 v2 R1 5 41 2 o a a 200 40 0 R 200 40 v v o 40 41 40 41 The correct answer is (C). 32
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
Example: Op Amp, Decibels A A 20log db v,diff 10 V in,1 V 40 V V 0 1 2 db v,diff 10 Vout V in,2 20log 40 32 db The correct answer is (A). 34 A A A A db db db db p p,1 p,2 p,3 100 25 9 134 db
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 10 30 2 j 0.1 3 kω j 0.1 3 kω 1 kω 35 input (x) = voltage, output (y) = voltage, system (h) = voltage divider
Example: Transfer Function 36
Example: Transfer Function v 1 Vo v1 Vin v1 0 v1 v2 0 20 MΩ 1 jc 5 MΩ v 2 V o in 20 MΩ 1 5MΩ 6 6 1 jc j 2 60.00110 j 2.7 10 V V o 20j 2.7 j 1 5 20 2.7 0.5382 jc V in The correct answer is (B). 37
Dr. Gregory J. Mazzaro Spring 2018 gmazzaro@citadel.edu Grimsley Hall, Room 312 843-953-0429 http://ece.citadel.edu/mazzaro THE CITADEL, THE MILITARY COLLEGE OF SOUTH CAROLINA 171 Moultrie Street, Charleston, SC 29409