ece159s_2005_exam - UNIVERSITY OF TORONTO FACULTY OF...

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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 non-programmable 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 01-19 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 a-b. 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 x-y plane, and an infinite line of charge which lies on the z-axis, 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 z-axis. 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 a-b. [3 marks] (c) Calculate the maximum power that can be delivered to the load (RL) across terminals a-b 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 first-order 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.

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ece159s_2005_exam - UNIVERSITY OF TORONTO FACULTY OF...

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