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Unformatted text preview: UNIVERSITY OF TORONTO FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAMINATION, APRIL 2005 First Year —— Engineering Science ECE 1598  ELECTRICITY & ELECTRIC CIRCUITS Exam Type: A Examiners: M.L.G. Joy and NP. Kherani NAME: Last First STUDENT NO: INSTRUCTIONS:  This is a Type A examination; no aids are allowed.  Only nonprogrammable calculators are allowed.  Answer all parts of all ten questions.  All ten questions are of equal weight, though not of equal level of difficulty.
. All work is to be done on the pages of this booklet.  When answering the questiOns include all the steps of your work on these
pages. For additional space, you may use the back of the preceding page.  Do not unstaple this exam booklet. CONSTANTS: e = 1.6x10'19 0 60:8.85X10’12 CZ/(Nmz) yo=4nx10'7 Tm/A Page 1 of 11 Name: Student No.2 QUESTION 1 [10 marks] Fill in the blanks, and circle TRUE or FALSE, as appropriate. Comment if you must. Each part
is worth 1 mark. ‘ (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) ECE 159 I 2005 All electrical and magnetic phenomena are related to a property of matter kn0wn as Materials in which charges cannot move readily are known as
At equilibrium the electric ﬁeld inside a conductor is Electric ﬁeld lines point in the direction of increasing electric potential, that is, from low potential to high potential.
TRUE / FALSE The dielectric constant of a material is a measure of its polarizability. TRUE / FALSE A lamp alights immediately upon turning on the light switch because electrons travel through the wires at close to the speed of light.
TRUE / FALSE Magnetic ﬁelds arise as a result of The input impedance across terminals 0119 of a circuit can be determined by calculating the V.
quotient ﬂ, where Vin and [in are the assumed voltage and current, respectively, at I.
m terminals ab.
TRUE / FALSE The capacitor is an Open circuit at DC and a short circuit at inﬁnite frequency.
TRUE / FALSE Maximum power is delivered to a load when its voltage and current are 45° out of phase.
TRUE / FALSE Page 2 of 11 Name: Student No.: Question 2 [10 marks] infinite sheet
of charge (0') Consider an infinite sheet of charge which
lies on the xy plane, and an infinite line of
charge which lies on the zaxis, as shown in
the figure on the right. The surface charge
density of the sheet has an unknown value
6 = 0'0 [C/mz], while the linear charge
density of the line is 9» = A0 [C/m]. of charge (1») (a) Now, place a cylindrical Gaussian surface
of radius r = a and length L = 2a
symmetrically about the origin such that
the axis of the cylinder is on the zaxis.
Given that the total electrical ﬂux through
the Gaussian surface is (Do, find the surface charge density 0'0 in terms of the
other variables. [5 marks] cylindrical
Gaussian surface (b) Now, let the dimensions r and L, of the cylindrical Gaussian surface be different than in part (a). Find the ratio R: rz/L, in terms of A0 and 0'0, so that the electrical ﬂux due to the line of
charge is equal to the electrical ﬂux due to the sheet of charge. [5 marks] ECE 159 I 2005 Page 3 of 11 Name: Student No.2 Question 3 [10 marks] A square loop of resistive wire with sides of length 0.1 m lies fixed in a plane in a uniform A magnetic ﬁeld. The unit vector n is normal to this plane. The speciﬁc resistance of the wire is 1000 ﬁlm. The magnetic ﬁeld E=0.05sin(1000t)k, where E is in tesla, t is the time in
1 JE seconds, and k is the unit vector along the positive z—axis. The unit vector n = (1,1,1) . (a) Compute the magnetic ﬂux, @(t), through the loop in the direction :1. State units. Show
method. [3 marks] (b) Compute the current, I, ﬂowing in the loop in the right hand sense with respect to the direction n. Assume that any magnetic ﬁeld arising from this current is negligible.
[4 marks] 4 —)
(0) Compute the torque vector, r , on the 100p due to the current I and the magnetic field B .
—) —) —) —) Note: I = ,ux B , where the magnetic moment ,u = IA n where A is the area of the loop.
[3 marks] ECE 159 I 2005 Page 4 of 1 1 Name: Student No.2 Question 4 [10 marks] A coaxial capacitor of length L has an inner conductor
radius of a, and an outer conductor of inner radius b.
The space between the conductors is filled with a dielectric material of relative permittivity 8,. Assume Dielectric, —)—> that E (r) , the electric ﬁeld in the capacitor (between r=a and r=b), is E(r)=————Q~———;, where
27I£08,Lr Q is the charge on the inner conductor, r is the radial perspective view cross—sectional view
__) A
position vector, r = r and r is the corresponding
unit vector. (a) Find the potential difference Vab = Va — Vb, where Va and Vb are the potentials at radii a
and b, respectively. [4 marks] (b) Find the capacitance of the coaxial capacitor. [3 marks] (c) If the dielectric material is Teﬂon which has a dielectric strength of K [V/m], ﬁnd the
maximum potential difference across the capacitor, Vabmax, before breakdown. [3 marks] ECE 159 I 2005 Page 5 of 11 Name: Student No.2 Question 5 [10 marks] Consider the following DC circuit. (a) Find VR and IR in terms of V, I, and R when switch A is open.
HINT: The values of some of the components will not affect your answer.[2 marks] (b) Find VR and IR in terms of V, I, and R when switch A is closed.
HINT: The values of some of the components will not affect your answer. [5 marks ] (c) Given that V > O and I > 0 in part (b), what is the coustraint on the value of R so that the
voltage scurce V is supplying power? Express the constraint as an inequality in terms of V, R and I.
[3 marks ] ECE 159 / 2005 Page 6 of 11 Name: Student No.: Question 6 [10 marks] Consider the following DC circuit.
l HINT: The values of some of the components will not affect your answer. 50 nF 5 k!) 100 trH (a) Find the Thévenin equivalent source (voltage), VTH, with respect to terminals a—b.
[4 marks] (b) Find the Thévenin equivalent resistance, Rm, with respect to terminals ab. [3 marks] (c) Calculate the maximum power that can be delivered to the load (RL) across terminals ab
and the magnitude of the load? [3 marks] ECE 159 I 2005 Page 7 of 11 Name: Student No.: QUESTION 7 [10 marks] Consider the differential ampliﬁer circuit shown
on the right. Assume that the operational
ampliﬁers are ideal. The differential input to the circuit is defined as Vin: VX Vy. The differential output from the
circuit is defined as Vow: Vox V0y. (a) Set Vy = 0, while maintaining Vx on, and ﬁnd Vox(") and V031“). [4 marks] (b) Now set Vx = 0, while maintaining Vy on, and find Voxﬂ’) and V0y(b). [4 marks] V0 (c) Now ﬁnd the differential gain, G = in ECE 159 l 2005 “’ , of the differential amplifier. [2 marks] Page 8 of 11 Name: Student No.1 QUESTION 8 [10 marks] Consider the following ﬁrstorder transient circuit. Assume that the circuit is in steady state prior to the switching action at time t = 0. At time t = 0, the switch is closed. *15V+ 400w7 a) Find i(t) for t = 0' and t = 0*. [5 marks] b) Find i(t) after the switch has been closed for a long time, i.e., ast > oo. [2 marks] c) What is the time constant with which i(t) decays? [2 marks] (1) Write the expression fOr i( t) for t>0. [1 mark] ECE 159/2005 Page 9 of 11 Name: Student No.: QUESTION 9 [10 marks] Consider the following AC circuit. 1009 VA 0.01 H 4.. vs( t) = 100 cos(1000t) SOuF R=10€2 (a) Draw the above circuit in the frequency domain, i.e., using phasors and impedances rather than resistors, capacitors and inductors. [2 marks] (b) Calculate the voltage phasor 11,4. [5 marks] (0) Calculate the real power and reactive power delivered to the branch containing the 0.01H
inductor in series with the 109 resistor. Also, calculate the power factor of the load. [3 marks] ECE 159/ 2005 Page 10 of 11 Name: , Student No.: QUESTION 10 [10 marks] Consider the circuit on the right. The values of the various loads and sources are given below. C =1uF
L=2.5mH
R=SOQ V510) = cos(104 t) V520): ﬁsin(2x104t) Note the different frequencies. (a) Step 1: Find the impedance of the capacitor C, Zc, and of the inductor L, ZL,for m =
104rad/s. [1 mark] Step 2: Replace V32 with a short, that is, turn off V32. Find the impedance Z" (at 0) = 104
rad/s) as seen by V51? [2 marks] Step 3: Find l_/L (in phasor form) due to Vs] only? [2 marks] Note: Use voltage division to write l_/L in terms of Zis and KS 1, where i=R, C, L. (b) What is XL (in phasor form) due to V32 only? Proceed as in part (a). [4 marks] (0) What is VL in the time domain, considering both sources are on simultaneously? [1 mark] ECE 159 I 2005 Page 11 of 11 ...
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This test prep was uploaded on 04/18/2008 for the course ENGINEERIN ece159 taught by Professor B.wang during the Winter '08 term at University of Toronto.
 Winter '08
 B.wang

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