UNIVERSITY OF BOLTON SCHOOL OF ENGINEERING B.ENG (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATION SEMESTER /2018

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1 ENG005 B.ENG (HONS) ELECTRICAL AND ELECTRONIC ENGINEERING EXAMINATION SEMESTER 1-017/018 MODULE NO: EEE4001 Dte: 19Jnury 018 Time: INSTRUCTIONS TO CANDIDATES: There re SIX questions. Answer ANY FOUR questions. All questions crry equl mrks. Mrks for prts of questions re shown in brckets. Electronic clcultors my be used provided tht dt nd progrm storge memory is clered prior to the emintion. CANDIDATES REQUIRE: Formul Sheet (ttched).

2 Pge of 11 EXAMINATION SEMESTER 1-017/018 Q1 () The eqution of the Common Mode Rejection Rtio (CMRR) of n opertionl mplifier cn be given s: CMRR = 0 1og 10 ( A d A cm ) Where A d is the differentil gin nd A cm is the common mode gin. Given tht CMRR is 86 db, find the rtio of A d A cm. (b) Fctorise the following epression: (c) Solve the eqution 3 ln = (d) Epress 6 in prtil fctions (e) Find the cross product of vectors A nd B, where A = (,3,4) nd B=(5,6,7) Totl 5 mrks

3 Pge 3 of 11 EXAMINATION SEMESTER 1-017/018 Q. () Consider the following mtrices: 1 A B C 1 (Hint: Eplin which of the following opertions mke sense. Evlute the ones tht do.) i) B T A ii) C -1 B iii) C B -1 (b) Solve the following trigonometric eqution for : cot cos = cot (c) Find the sum of the following series: Totl 5 mrks

4 Pge 4 of 11 EXAMINATION SEMESTER 1-017/018 Q3. The following four comple numbers re given by: Z 1 = + i, Z = 1 i, Z 3 = cis70 0 π i nd Z 4 = e where i 1. () Clculte z1 z nd epress the solution in polr form (b) Epress the product z z 1 3 in rectngulr form (c) Find the comple conjugte for z3 nd z4 (d) Find the rel nd imginry prts of the rtio z z 4 (e) Clculte (Z1) 4 nd epress the nswer in eponentil form Totl 5 mrks

5 Pge 5 of 11 EXAMINATION SEMESTER 1-017/018 Q4 () Given tht f ( ) sin tn, show tht f 4 [10 mrks] (b) A body is moving in stright line, so tht fter t seconds its displcement metres from fied point O, is given by displcement, velocity nd ccelertion. 3 43t 7t 6t. Find the initil (c) Prove tht d cosec cosec cot [9 mrks] [6 mrks] Totl 5 mrks Q5. Evlute the following integrls: 3 () 3 + e (b) (c) ln 3 [8 mrks] [7 mrks] e [10 mrks] Totl 5 mrks

6 Pge 6 of 11 EXAMINATION SEMESTER 1-017/018 Q6 () Find the time dependence of the electric current i(t) of the given LR circuit s shown in Fig. 6(). Given tht L= mh, R= 10 Ω nd U is 5 v. di L Ri U dt Where U is the voltge, R is the resistor, i is the current nd L is the inductor. Fig.6(): A series LR electricl circuit. (b) The differentil eqution of series RLC circuit is given s below: [1 mrks] v d v dt C LC dv RC dt C v C Where v is the voltge source, L is the inductor, C is the cpcitor, Vc is the voltge cross the cpcitor, nd R is the resistor. Assuming v =0, L= 1 mh, C= 10 µf, R=0 Ω, find the time dependence of the voltge cross the cpcitor Vc(t). [13 mrks] Totl 5 mrks END OF QUESTIONS

7 Pge 7 of 11 EXAMINATION SEMESTER 1-017/018 Formul sheet The following formule my be used without proof. Differentition Integrtion f() f () f() f () n 1 n n n 1 n C n 1 n 1 ln 1 1 ln + C e e e e + C sin cos sin cos + C cos sin cos sin + C cosec cosec cot sec tn sec sec sec tn cosec cot cosec LIPET -Logs, Inverse trigonometry, Polynomil, Eponentil, Trigonometry y uv Product Rule dy dv u v du y u v Quotient Rule du dv v u dy v y f(u ), u Chin Rule dy g( ) dy du du Integrtion by Prts dv du u uv v Two Integrtion Formuls

8 Pge 8 of 11 EXAMINATION SEMESTER 1-017/018 n 1 n1 (f( )) f' ( ) (f( )) c, n 1 nd n 1 f' ( ) ln(f( )) c, f( ) 0 f( ) b The Volume of Revolution y, where y f( ) for rottion of bout the - is. The centroid of region bounded by the curve y = f() nd the lines = nd = b is given by b b f ( ) f( ) nd y b f( ) b f( ) Newton Rphson method for estimting the solution for f() = 0. n1 n f ( f '( n n ) ) Trpezium Rule with n intervls of length h. h f ( ) f( 0 ) f( 1 ) f( ) f( n 1 ) f( n ) Tylor series ( ) ( ) f ( ) f ( ) ( ) f '( ) f ''( ) f '''( )! 3! De Moivre s Theorem 3

9 Pge 9 of 11 EXAMINATION SEMESTER 1-017/018 Finite Arithmetic Finite Geometric Infinite Geometric Finite Arithmetic Finite Geometric Infinite Geometric L Hôpitl s rule for finding limiting vlues f ( ) f ( ) Lim Lim g( ) g( ) The Rtio Test for series lim n n1 n If The series converges if ρ < 1, The series diverges if ρ > 1, The test is inconclusive if ρ = 1.

10 Pge 10 of 11 EXAMINATION SEMESTER 1-017/018 Inverse mtri: Qudrtic formul: The generl formul for first order inhomogenous liner differentil eqution is: dy + Py = Q The generl solution of the bove inhomogeneous eqution is: y e P Where e P() is the integrting fctor. P ( K Qe ) The generl formul for second order differentil eqution is: y' ' by' cy 0 y e

11 Pge 11 of 11 EXAMINATION SEMESTER 1-017/018 b c 0 1 b b 4c y( ) e [ C cos C sin ] 1

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